Segmentation Targeting and Positioning of Vodafone

Segmentation Targeting and Positioning of Vodafone Vodafone is one of the biggest names in wireless technology, and is continuing to grow a solid, loyal customer base because the company offers excellent product along with excellent customer service. Vodafone has a an interesting history, back to 1984, when it was still a subsidiary of the well-known Racal Electronics Plc. In September 1991, the Vodafone Group Plc decided to separate itself from Racal Electronics Plc, they later merged with another company, the Air Touch Communications Inc, in July 2000. In 2001, this wireless company first introduced instant messaging on their networks, to provide for a faster way to communicate among their users. The company also launched the first ever 3G service in Europe with their innovative mobile connect GPRS/3G data card in 2004. In February 2007, the company had another major milestone when it partnered with Yahoo and Microsoft in order to launch instant messaging services that can easily be accessed using either a personal computer or a mobile phone. This is one of the milestones that made it into the wireless giant it is today. The company continues to offer a variety of services, including data, messaging, voice and broadband. Its continuous advancement in the data services, they offer by developing its 3G networks and the capabilities of various handsets. Its a mobile service thats easy to use, with low-cost telephone line and even DSL broadband connection.It also provides you monthly billing cycle,pre-paid agreement or even a contract.And is known for its best customer services. BACKGROUND:-(INTERNATIONAL EXPANSION STRATEGIES). Vodafone Group Plc is the worlds leading International mobile telecommunications Group, with a major presence in Europe, the Middle East, Africa, Asia Pacific and the United States through the Companys subsidiary undertakings, joint ventures, associated undertakings and investments. The basic concept of this case is to look at Vodafones future expansion, growth and global strategies within the concept of internationalization and competitive advantage issues.The reason to launch Vodafone in Mexican market is to gain profitibility,gaining high revenues by doing better business in more areas or internationally.Because if Vodafone will not be launched in Mexico some other mobile company will do the same.Being one of the worlds largest company its easy for Vodafone to enter the Mexican market and capture it. PESTEL ANALYSIS:- It is the technique of environmental scanning of any industry on the basis of factors like political, economic, social, technological, legal and environmental. PESTLE analysis uses a framework of external factors for macro-environmental scanning of the industry to help in taking advantage of opportunities and making contingency plans for threats. SEGMENTATION, TARGETING AND POSITIONING:- It together comprise a three stage process; Segmentstion (identifying meaningfully different groups of customers) Targating (selecting which segment to serve) Positioning (implementing chosen image and appeal to chosen segment) it furthur includes product,price,distribution and promotion. SEGMENTATION:- Segmentation is the process of splitting (segmenting) the entire market into smaller groups. Demographics is the most common variable of market segmentation that includes age, gender, income, geographic, psychograhpic and behavioural.For launching a Vodafone in Mexican market, the product is for both the genders ,of evry area with variaing ages and incomes. Markets are made up of many distinct groups of people who have common characteristics as consumers. Some of those groups may not be immediately obvious. All of them command tremendous buying power. But they direct it to products and services that address them as a highly individual subdivision or segment of the market. Define those market segments right and you may even end up dominating the market. Because the more you know about a market segment: The better you can provide a product or service that attracts it. The better you can create marketing materials that appeal to it. The more cost-effectively you can direct them at the markets that respond the best. The easier it is to position your company and product and build brand loyalty. Its hard to successfully address a large, vague, undifferentiated market. Its easy to address a tightly focused, highly individualized group of people with clearly defined preferences and needs. Market segmentation isolates those groups, and makes them accessible. It helps your organization understand them and reach them and profit too. TARGETING:- In this step one or more segment is targeted.Generally depend on several factors. How well are existing segments served by other manufacturers? How large is the segment, and how can we expect it to grow? Do we have strengths as a company that will help us appeal particularly to one group of consumers? It will be more difficult to appeal to a segment that is already well served than to one whose needs are not currently being served well.Mexican market is already being served well but Vodafone being a giant can capture the market by providing equally better or more advanced services. POSITIONING:- Positioning basically involves implementing the targeting. Product (premium,basic) Price (premium,low price,value) Distribution (intensive,selective,exclusive) Promotion (prestige,fun,powerful) Being operationally excellent firm,by maintaing exceptional efficiency,the firm providing reliable service to the customer at a significantly lower cost. Vodafone can capture the market.Its customer intimate firm which excel in serving the specific needs of the individual customer quiet well. Technologically it is prodviding the most advanced products currently available. COMPETATOR ANALYSIS AND MARKET ENTRY STRATEGY:- Its a critical part of firms activities.Competitor analysis has several important roles in strategic planning; It helps management to understand their competitive advantages/disadvantages relative to competitors. It generate understanding of competitors past, present andfuture strategies. It gives an informed basis to develop strategies to achieve competitive advantage in the future. Also help forecast the returns that are made from future investments i.e how will competitors respond to a new product or pricing strategy? Entering a new market is always a challange.The size of the country, number of opportunities and geographical size matters precisely.Solid market entry strategy needs proper market research to know existing opportunities, understand the competitive landscape and to know about potential clients.A market entry strategy has to be developed that fits companies objectives, timelines and budget. A successful Market Entry Strategy includes, assessing the feasibility of the product in market, what are the industry trends, what potential competitors are doing and what pains clients are facing that can address. If the market research reveals a robust opportunity, then it is time to develop your market entry strategy with a trusted partner that can not only write the strategy, but also help you implement it, in market.

Experience of the Attawapiskat Cree to Ojibwa in relation to the Canadian Government

The Attawaspiskat Cree and Ojibwa are a first nations group living in parts of Canada, mainly northern Ontario. The main languages spoken by these first nation groups are Mushkegowuk Cree and Ojibway. I will compare and contrast the experience of the Attawapiskat Cree to Ojibwa in relation to the Canadian Government. This will include analyzing the treaties introduced by the government towards the Cree and the Ojibwa: in particular, treaty 9 will be discussed. In addition, to these treaties the government has divided the first nation community into two different groups: status-Indians and non-status Indians. Within these two groups further division has been accomplished by the allocation of lands know as reserves to status-Indians and independent ownership for non-status Indians. This allocation of lands in reserves for status-Indians and independent ownership for non-status Indian is based on the policies developed through dependent and independent tenure. The laws permitting only status-Indians to live in reserves have fragmented the community and changes in culture and traditions have been rapid since the arrival of the government. The arrival of the Canadian government in the early nineteen-hundreds was the last major encapsulating factor the Cree and the Ojibwa were to face after the Hudson Bay Company and the church. The methods adopted by the government were aimed at changing the social, economic, political and religious practices held within these societies. One of the first efforts undertaken by the Canadian government was to legalize any action it would take in the regions occupied by the Cree and the Ojibwa. Therefore, in 1905 and 1906 treaty 9 was signed with the people of Cree and the people of Ojibwa. With the introduction of treaty 9, logging, hydroelectric development, minerals, construction of road and railways started. This treaty also introduced new land policies, which allowed non-Indians to exploit the resources used before only by the Indians. Commissioner Scott who represented the government promised the Indians that treaty 9 would not affect the way of living for the Indian people, rather the government would help in times of need: â€Å"There will not be any legislation governing trapping, hunting animals and hunting birds and fishing, if you are in favour of the treaty. If something happens to you as to sickness or need of help the government will help you, all the people from Albany, Attawapiskat, Winisk, Fort Severn, will have this help† (Cummins 2004, 36). However, during the famine of 1909, 1928, 1930-31, 1934-36 and 1946-48 in Attawaspiskat, assistance from the government was little or non-existent. Therefore, the main reason for the treaty was to extinguish aboriginal rights and to take away the land owned by the Indians. Following treaty 9 many different treaties were introduced by the government which further deteriorated the economical conditions present within the Indian community. These treaties had assured for the Cree and the Ojibwa, that provision would be made for the supply of seed, cattle and agricultural implements as these nations had exhibited an interest in starting farming for economic interest. Additionally, some other treaties had guaranteed distribution of fishing nets, net twins, guns and ammunition so as it can enable the Indians to hunt for subsistence activities, with participation with the new economy. However, the government provided insufficient amenities which were unable to economically improve the position of the Cree and Ojibwa. In addition, federal legislation – especially the Indian Act – teamed with federal and provincial policy and actions, rendered it arduous for Aboriginal people to undertake other economic interest. (http://www. ainc-inac. gc. ca/ch/rcap/sg/sh45_e. html). It is essential to define the terms land tenure and land use in order to understand how these systems are used as an encapsulating factor for the Ojibwa and the Attawapiskat Cree. Land use is the physical exploitation of land, where as land tenure are the policies which govern the use of land and is based on social, political and exploitative patterns of a group. Example of social, political and exploitative patterns would include the ways of accommodation, such as living in micro or macro bands and occupying a river drainage or a good fishing site; notion of land ownership; and hunting patters, respectively. Since the incursion of Euro-Canadians in all aspect of Indian life, there have been changes in the traditional land tenure policies held within these societies for centuries. The government has divided the Ojibwa and the Cree into two different categories: status Indians and non-status Indians. Status Indians are those individuals who according to the Indian Act appear on the governments list of registered Indians. Status-Indians are solely dependent on governmental aid and live on lands turned into reserves by the government; they are also exempted from any provincial or federal programs such as income tax and property tax. Non-status Indians are those who have lost their Indian status by governmental enfranchisement. These people cannot live on reserves; land setup by the government for status-Indians, but they can independently own land and must pay taxes. The reserves are created by the Indian Act as, â€Å"the minister may, when he considers it desirable constitute new bands and when a new band has been established from an existing band or any part thereof, such portion of the reserve lands and funds of the existing band as the minister determines shall be held for the use and benefit of the new band†. (Driben 1986: 114). Therefore, to create a reserve there must be, a new band who has requested the government to be turned into a reserve. Hence, if approved the government would allocate an existing reserve or some land. Once designated as a reserve, individuals cannot have the title to the land and cannot exercise the freedom to move fluidly in different areas or groups. One major set back by the government to the Ojibwa people living in Aroland are the economic government policy adopted towards them. In 1971, the provincial plan for economic development was revealed, which concluded that land and resource development should take place only in places which demonstrate a potential for growth. Therefore, the problem arouse when Nakina, a town less than 25 kilometres from Aroland became the centre of growth, this has shifted any incentives from private and government sectors to economically invest in Aroland. The government of Canada has introduced two types of land tenure for the Cree and the Objiwa, dependent and independent land tenure. In dependent land tenure two aspects must be fulfilled, first that region must be made into a reserve, and second, the people occupying the region must be status-Indians. Once the region has become a reserve it falls under the jurisdiction of the ministry of Indian Affairs. Therefore, by the Indian Act, the ministry has the authority to possess land, prevent the transfer of land between bands, and to allocate land as they see fit. The economic impact of the dependent tenure has its benefits and disadvantages. These benefits include that the ministry of Indian affairs will provide aid for economic development. Such aid can be in forms of loans to bands, groups or individuals. Moreover, the Indians are not required to pay property tax or income tax on the money they earn by working on the reserves. A disadvantage would be that the reserved land cannot be sold or leased unless it is surrendered to the government, and once the land has been surrendered to the government, it is controlled and owned by the government not the Indians. The social impact of dependent tenure is the segregation caused by the subdivision of Indians into status and non-status Indians. Therefore, to choose dependent tenure would segregate the community into one group, that comprising of status-Indians only. By the Indian act, non-status Indians are considered to be trespassers if they enter a reserve and can be fined and imprisoned for doing so. On the other hand, Independent Land Tenure is a more euro-Canadian form of land policy. Indians in independent land tenure can buy property. But if the people opt for Independent Land tenure they cannot form any kind of reserve. Since Independent tenure is regulated under provincial government, the federal government would not be involved. Once the provincial government sells the people the land they occupy, the individual will get the title to the land and also some benefits as stated by the minister, â€Å" Firstly, a surface right, which permits a landowner to enjoy the current use of his land. Secondly, a productive right, which allows an owner to make a profit from the current use of his land. Thirdly, a development right, allowing the owner to improve his property. Fourthly, a pecuniary right, whereby a landowner benefits financially from development value both effectively granting the right not to develop and sixthly, a disposal right, allowing an owner to sell or will his land† (Driben 1986: 105). The economic advantage of independent tenure is that Indians can participate in government programs, can be endowed with equity that can be employed to obtain mortgages and loans from banks and other financial institutions. Additionally they can have provincially tax-supported services such as fire protection, construction of roads, as well as other provincial benefits. In conclusion, the arrival of the government in the early nineteen-hundred marked a beginning which has rapidly cause change and encapsulated the Ojibwa and the Cree. Treaty 9, also known as the James Bay treaty, has let the government occupy two-third of northern Ontario from the Indians. An encapsulation method adopted by the government was to divide the Indians into different groups; this was done by dividing the people into status-Indians and non-status Indians. Further, physical sub-division was accomplished by the government through dependent and Independent tenure. Laws forbidding non-status Indians to enter reserves were strictly enforced and any economic incentives approached by the Indians were tentatively dealt with. Therefore the nineteen hundred has been a drastic change for the Ojibwa and the Cree, and it has transformed them from a simpler life of hunting for subsistence to that of trading and has made them conform to the external pressure to acculturate. BIBLIOGRAPHY Cummins, Brian D. 2004. Only God Can Own the Land. Toronto: Pearson Education Canada Inc. Driben, Paul. 1986. Aroland Is Our Home – An incomplete victory in Applied Anthropology. New York: AMS Press. Martin, Calvin. 1978. Keepers of the Game. Berkeley, Los Angeles, London: University of California Press. Schmalz, Peter S. 1991. The Ojibwa. Toronto, Buffalo, and London: University of Toronto Press. Krech, Shepard. 1981. Indians, Animals, and the Fur trade. Athens: The University of Georgia Press. .

Bag of Bones CHAPTER TWENTY-ONE

I was walking north along The Street. Japanese lanterns lined it, but they were all dark because it was daylight bright daylight. The muggy, smutchy look of mid-July was gone; the sky was that deep sapphire shade which is the sole property of October. The lake was deepest indigo beneath it, sparkling with sunpoints. The trees were just past the peak of their autumn colors, burning like torches. A wind out of the south blew the fallen leaves past me and between my legs in rattly, fragrant gusts. The Japanese lanterns nodded as if in approval of the season. Up ahead, faintly, I could hear music. Sara and the Red-Tops. Sara was belting it out, laughing her way through the lyric as she always had . . . only, how could laughter sound so much like a snarl? ‘White boy, I'd never kill a child of mine. That you'd even think it!' I whirled, expecting to see her right behind me, but there was no one there. Well . . . The Green Lady was there, only she had changed her dress of leaves for autumn and become the Yellow Lady. The bare pine-branch behind her still pointed the way: go north, young man, go north. Not much farther down the path was another birch, the one I'd held onto when that terrible drowning sensation had come over me again. I waited for it to come again now for my mouth and throat to fill up with the iron taste of the lake but it didn't happen. I looked back at the Yellow Lady, then beyond her to Sara Laughs. The house was there, but much reduced: no north wing, no south wing, no second story. No sign of Jo's studio off to the side, either. None of those things had been built yet. The ladybirch had travelled back with me from 1998; so had the one hanging over the lake. Otherwise ‘Where am I?' I asked the Yellow Lady and the nodding Japanese lanterns. Then a better question occurred to me. ‘When am I?' No answer. ‘It's a dream, isn't it? I'm in bed and dreaming.' Somewhere out in the brilliant, gold-sparkling net of the lake, a loon called. Twice. Hoot once for yes, twice for no, I thought. Not a dream, Michael. I don't know exactly what it is spiritual time-travel, maybe but it's not a dream. ‘Is this really happening?' I asked the day, and from somewhere back in the trees, where a track which would eventually come to be known as Lane Forty-two ran toward a dirt road which would eventually come to be known as Route 68, a crow cawed. Just once. I went to the birch hanging over the lake, slipped an arm around it (doing it lit a trace memory of slipping my hands around Mattie's waist, feeling her dress slide over her skin), and peered into the water, half-wanting to see the drowned boy, half-fearing to see him. There was no boy there, but something lay on the bottom where he had been, among the rocks and roots and waterweed. I squinted and just then the wind died a little, stilling the glints on the water. It was a cane, one with a gold head. A Boston Post cane. Wrapped around it in a rising spiral, their ends waving lazily, were what appeared to be a pair of ribbons white ones with bright red edges. Seeing Royce's cane wrapped that way made me think of high-school graduations, and the baton the class marshal waves as he or she leads the gowned seniors to their seats. Now I understood why the old crock hadn't answered the phone. Royce Merrill's phone-answering days were all done. I knew that; I also knew I had come to a time before Royce had even been born. Sara Tidwell was here, I could hear her singing, and when Royce had been born in 1903, Sara had already been gone for two years, she and her whole Red-Top family. ‘Go down, Moses,' I told the ribbon-wrapped cane in the water. ‘You bound for the Promised Land.' I walked on toward the sound of the music, invigorated by the cool air and rushing wind. Now I could hear voices as well, lots of them, talking and shouting and laughing. Rising above them and pumping like a piston was the hoarse cry of a sideshow barker: ‘Come on in, folks, hurr-ay, hurr-ay, hurr-ay! It's all on the inside but you've got to hurr-ay, next show starts in ten minutes! See Angelina the Snake-Woman, she shimmies, she shakes, she'll bewitch your eye and steal your heart, but don't get too close for her bite is poy-son! See Hando the Dog-Faced Boy, terror of the South Seas! See the Human Skeleton! See the Human Gila Monster, relic of a time God forgot! See the Bearded Lady and all the Killer Martians! It's on the inside, yessirree, so hurr-ay, hurr-ay, hurr-ay!' I could hear the steam-driven calliope of a merry-go-round and the bang of the bell at the top of the post as some lumberjack won a stuffed toy for his sweetie. You could tell from the delighted feminine screams that he'd hit it almost hard enough to pop it off the post. There was the snap of. 22s from the shooting gallery, the snoring moo of someone's prize cow . . . and now I began to smell the aromas I have associated with county fairs since I was a boy: sweet fried dough, grilled onions and peppers, cotton candy, manure, hay. I began to walk faster as the strum of guitars and thud of double basses grew louder. My heart kicked into a higher gear. I was going to see them perform, actually see Sara Laughs and the Red-Tops live and on stage. This was no crazy three-part fever-dream, either. This was happening right now, so hurr-ay, hurr-ay, hurr-ay. The Washburn place (the one that would always be the Bricker place to Mrs. M.) was gone. Beyond where it would eventually be, rising up the steep slope on the eastern side of The Street, was a flight of broad wooden stairs. They reminded me of the ones which lead down from the amusement park to the beach at Old Orchard. Here the Japanese lanterns were lit in spite of the brightness of the day, and the music was louder than ever. Sara was singing ‘Jimmy Crack Corn.' I climbed the stairs toward the laughter and shouts, the sounds of the Red-Tops and the calliope, the smells of fried food and farm animals. Above the stairhead was a wooden arch with WELCOME TO FRYEBURG FAIR WELCOME TO THE 20TH CENTURY printed on it. As I watched, a little boy in short pants and a woman wearing a shirtwaist and an ankle-length linen skirt walked under the arch and toward me. They shimmered, grew gauzy. For a moment I could see their skeletons and the bone grins which lurked beneath their laughing faces. A moment later and they were gone. Two farmers one wearing a straw hat, the other gesturing expansively with a corncob pipe appeared on the Fair side of the arch in exactly the same fashion. In this way I understood that there was a barrier between The Street and the Fair. Yet I did not think it was a barrier which would affect me. I was an exception. ‘Is that right?' I asked. ‘Can I go in?' The bell at the top of the Test Your Strength pole banged loud and clear. Bong once for yes, twice for no. I continued on up the stairs. Now I could see the Ferris wheel turning against the brilliant sky, the wheel that had been in the background of the band photo in Osteen's Dark Score Days. The framework was metal, but the brightly painted gondolas were made of wood. Leading up to it like an aisle leading up to an altar was a broad, sawdust-strewn midway. The sawdust was there for a purpose; almost every man I saw was chewing tobacco. I paused for a few seconds at the top of the stairs, still on the lake side of the arch. I was afraid of what might happen to me if I passed under. Afraid of dying or disappearing, yes, but mostly of never being able to return the way I had come, of being condemned to spend eternity as a visitor to the turn-of-the-century Fryeburg Fair. That was also like a Ray Bradbury story, now that I thought of it. In the end what drew me into that other world was Sara Tidwell. I had to see her with my own eyes. I had to watch her sing. Had to. I felt a tingling as I stepped beneath the arch, and there was a sighing in my ears, as of a million voices, very far away. Sighing in relief? Dismay? I couldn't tell. All I knew for sure was that being on the other side was different the difference between looking at a thing through a window and actually being there; the difference between observing and participating. Colors jumped out like ambushers at the moment of attack. The smells which had been sweet and evocative and nostalgic on the lake side of the arch were now rough and sexy, prose instead of poetry. I could smell dense sausages and frying beef and the vast shadowy aroma of boiling chocolate. Two kids walked past me sharing a paper cone of cotton candy. Both of them were clutching knotted hankies with their little bits of change in them. ‘Hey kids!' a barker in a dark blue shirt called to them. He was wearing sleeve-garters and his smile revealed one splendid gold tooth. ‘Knock over the milk-bottles and win a prize! I en't had a loser all day!' Up ahead, the Red-Tops swung into ‘Fishin Blues.' I'd thought the kid on the common in Castle Rock was pretty good, but this version made the kid's sound old and slow and clueless. It wasn't cute, like an antique picture of ladies with their skirts held up to their knees, dancing a decorous version of the black bottom with the edges of their bloomers showing. It wasn't something Alan Lomax had collected with his other folk songs, just one more dusty American butterfly in a glass case full of them; this was smut with just enough shine on it to keep the whole struttin bunch of them out of jail. Sara Tidwell was singing about the dirty boogie, and I guessed that every overalled, straw-hatted, plug-chewing, callus-handed, clod-hopper-wearing farmer standing in front of the stage was dreaming about doing it with her, getting right down to where the sweat forms in the crease and the heat gets hot and the pink comes glimmering through. I started walking in that direction, aware of cows mooing and sheep blatting from the exhibition barns the Fair's version of my childhood Hi-Ho Dairy-O. I walked past the shooting gallery and the ringtoss and the penny-pitch; I walked past a stage where The Handmaidens of Angelina were weaving in a slow, snakelike dance with their hands pressed together as a guy with a turban on his head and shoepolish on his face tooted a flute. The picture painted on stretched canvas suggested that Angelina on view inside for just one tenth of a dollar, neighbor would make these two look like old boots. I walked past the entrance to Freak Alley, the corn-roasting pit, the Ghost House, where more stretched canvas depicted spooks coming out of broken windows and crumbling chimneys. Everything in there is death, I thought . . . but from inside I could hear children who were very much alive laughing and squealing as they bumped into things in the dark. The older among them were likely stealing kisse s. I passed the Test Your Strength pole, where the gradations leading to the brass bell at the top were marked BABY NEEDS HIS BOTTLE, SISSY, TRY AGAIN, BIG BOY, HE-MAN, and, just below the bell itself, in red: HERCULES! Standing at the center of a little crowd a young man with red hair was removing his shirt, revealing a heavily muscled upper torso. A cigar-smoking carny held a hammer out to him. I passed the quilting booth, a tent where people were sitting on benches and playing Bingo, the baseball pitch. I passed them all and hardly noticed. I was in the zone, tranced out. ‘You'll have to call him back,' Jo had sometimes told Harold when he phoned, ‘Michael is currently in the Land of Big Make-Believe.' Only now nothing felt like pretend and the only thing that interested me was the stage at the base of the Ferris wheel. There were eight black folks up there on it, maybe ten. Standing at the front, wearing a guitar and whaling on it as she sang, was Sara Tidwell. She w as alive. She was in her prime. She threw back her head and laughed at the October sky. What brought me out of this daze was a cry from behind me: ‘Wait up, Mike! Wait up!' I turned and saw Kyra running toward me, dodging around the strollers and gamesters and midway gawkers with her pudgy knees pumping. She was wearing a little white sailor dress with red piping and a straw hat with a navy-blue ribbon on it. In one hand she clutched Strickland, and when she got to me she threw herself confidently forward, knowing I would catch her and swing her up. I did, and when her hat started to fall offi caught it and jammed it back on her head. ‘I taggled my own quartermack,' she said, and laughed. ‘Again.' ‘That's right,' I said. ‘You're a regular Mean Joe Green.' I was wearing overalls (the tail of a wash-faded blue bandanna stuck out of the bib pocket) and manure-stained workboots. I looked at Kyra's white socks and saw they were homemade. I would find no discreet little label reading Made in Mexico or Made in China if I took off her straw hat and looked inside, either. This hat had been most likely Made in Motton, by some farmer's wife with red hands and achy joints. ‘Ki, where's Mattie?' ‘Home, I guess. She couldn't come.' ‘How did you get here?' ‘Up the stairs. It was a lot of stairs. You should have waited for me. You could have carrot me, like before. I want to hear the music.' ‘Me too. Do you know who that is, Kyra?' ‘Yes,' she said, ‘Kito's mom. Hurry up, slowpoke!' I walked toward the stage, thinking we'd have to stand at the back of the crowd, but they parted for us as we came forward, me carrying Kyra in my arms the lovely sweet weight of her, a little Gibson Girl in her sailor dress and ribbon-accented straw hat. Her arm was curled around my neck and they parted for us like the Red Sea had parted for Moses. They didn't turn to look at us, either. They were clapping and stomping and bellowing along with the music, totally involved. They stepped aside unconsciously, as if some kind of magnetism were at work here ours positive, theirs negative. The few women in the crowd were blushing but clearly enjoying themselves, one of them laughing so hard tears were streaming down her face. She looked no more than twenty-two or -three. Kyra pointed to her and said matter-of-factly: ‘You know Mattie's boss at the liberry? That's her nana.' Lindy Briggs's grandmother, and fresh as a daisy, I thought. Good Christ. The Red-Tops were spread across the stage and under swags of red, white, and blue bunting like some time-travelling rock band. I recognized all of them from the picture in Edward Osteen's book. The men wore white shirts, arm-garters, dark vests, dark pants. Son Tidwell, at the far end of the stage, was wearing the derby he'd had on in the photo. Sara, though . . . ‘Why is the lady wearing Mattie's dress?' Kyra asked me, and she began to tremble. ‘I don't know, honey. I can't say.' Nor could I argue it was the white sleeveless dress Mattie had been wearing on the common, all right. On stage, the band was smoking through an instrumental break. Reginald ‘Son' Tidwell strolled over to Sara, feet ambling, hands a brown blur on the strings and frets of his guitar, and she turned to face him. They put their foreheads together, she laughing and he solemn; they looked into each other's eyes and tried to play each other down, the crowd cheering and clapping, the rest of the Red-Tops laughing as they played. Seeing them together like that, I realized that I had been right: they were brother and sister. The resemblance was too strong to be missed or mistaken. But mostly what I looked at was the way her hips and butt switched in that white dress. Kyra and I might be dressed in turn-of-the-century country clothes, but Sara was thoroughly modern Millie. No bloomers for her, no petticoats, no cotton stockings. No one seemed to notice that she was wearing a dress that stopped above her knees that she was all but naked by the standards of this time. And under Mattie's dr ess she'd be wearing garments the like of which these people had never seen: a Lycra bra and hip-hugger nylon panties. If I put my hands on her waist, the dress would slip not against an unwet-coming corset but against soft bare skin. Brown skin, not white. What do you want, sugar? Sara backed away from Son, shaking her ungirdled, unbustled fanny and laughing. He strolled back to his spot and she turned to the crowd as the band played the turnaround. She sang the next verse looking directly at me. ‘Before you start in fishin you better check your line. Said before you start in fishin, honey, you better check on your line. I'll pull on yours, darling, and you best tug on mine.' The crowd roared happily. In my arms, Kyra was shaking harder than ever. ‘I'm scared, Mike,' she said. ‘I don't like that lady. She's a scary lady. She stole Mattie's dress. I want to go home.' It was as if Sara heard her, even over the rip and ram of the music. Her head cocked back on her neck, her lips peeled open, and she laughed at the sky. Her teeth were big and yellow. They looked like the teeth of a hungry animal, and I decided I agreed with Kyra: she was a scary lady. ‘Okay, hon,' I murmured in Ki's ear. ‘We're out of here.' But before I could move, the sense of the woman I don't know how else to say it fell upon me and held me. Now I understood what had shot past me in the kitchen to knock away the CARLADEAN letters; the chill was the same. It was almost like identifying a person by the sound of their walk. She led the band to the turnaround once more, then into another verse. Not one you'd find in any written version of the song, though: ‘I ain't gonna hurt her, honey, not for all the treasure in the world'. Said I wouldn't hurt your baby, not for diamonds or for pearls Only one black-hearted bastard dare to touch that little girl.' The crowd roared as if it were the funniest thing they'd ever heard, but Kyra began to cry. Sara saw this and stuck out her breasts much bigger breasts than Mattie's and shook them at her, laughing her trademark laugh as she did. There was a parodic coldness about this gesture . . . and an emptiness, too. A sadness. Yet I could feel no compassion for her. It was as if the heart had been burned out of her and the sadness which remained was just another ghost, the memory of love haunting the bones of hate. And how her laughing teeth leered. Sara raised her arms over her head and this time shook it all the way down, as if reading my thoughts and mocking them. Just like jelly on a plate, as some other old song of the time has it. Her shadow wavered on the canvas backdrop, which was a painting of Fryeburg, and as I looked at it I realized I had found the Shape from my Manderley dreams. It was Sara. Sara was the Shape and always had been. No, Mike. That's close, but it's not right. Right or wrong, I'd had enough. I turned, putting my hand on the back of Ki's head and urging her face down against my chest. Both her arms were around my neck now, clutching with panicky tightness. I thought I'd have to bull my way back through the crowd they had let me in easily enough, but they might be a lot less amenable to letting me back out. Don't fuck with me, boys, I thought. You don't want to do that. And they didn't. On stage Son Tidwell had taken the band from E to G, someone began to bang a tambourine, and Sara went from ‘Fishin Blues' to ‘Dog My Cats' without a single pause. Out here, in front of the stage and below it, the crowd once more drew back from me and my little girl without looking at us or missing a beat as they clapped their work-swollen hands together. One young man with a port-wine stain swimming across the side of his face opened his mouth at twenty he was already missing half his teeth and hollered ‘Yee-HAW!' around a melting glob of tobacco. It was Buddy Jellison from the Village Cafe, I realized . . . Buddy Jellison magically rolled back in age from sixty-eight to eighteen. Then I realized the hair was the wrong shade light brown instead of black (although he was pushing seventy and looking it in every other way, Bud hadn't a single white hair in his head). This was Buddy's grandfather, maybe even his great-grandfather. I didn't give a sh it either way. I only wanted to get out of here. ‘Excuse me,' I said, brushing by him. ‘There's no town drunk here, you meddling son of a bitch,' he said, never looking at me and never missing a beat as he clapped. ‘We all just take turns.' It's a dream after all, I thought. It's a dream and that proves it. But the smell of tobacco on his breath wasn't a dream, the smell of the crowd wasn't a dream, and the weight of the frightened child in my arms wasn't a dream, either. My shirt was hot and wet where her face was pressed. She was crying. ‘Hey, Irish!' Sara called from the stage, and her voice was so like Jo's that I could have screamed. She wanted me to turn back I could feel her will working on the sides of my face like fingers but I wouldn't do it. I dodged around three farmers who were passing a ceramic bottle from hand to hand and then I was free of the crowd. The midway lay ahead, wide as Fifth Avenue, and at the end of it was the arch, the steps, The Street, the lake. Home. If I could get to The Street we'd be safe. I was sure of it. ‘Almost done, Irish!' Sara shrieked after me. She sounded angry, but not too angry to laugh. ‘You gonna get what you want, sugar, all the comfort you need, but you want to let me finish my bi'ness. Do you hear me, boy? Just stand clear! Mind me, now!' I began to hurry back the way I had come, stroking Ki's head, still holding her face against my shirt. Her straw hat fell off and when I grabbed for it, I got nothing but the ribbon, which pulled free of the brim. No matter. We had to get out of here. On our left was the baseball pitch and some little boy shouting ‘Willy hit it over the fence, Ma! Willy hit it over the fence!' with monotonous, brain-croggling regularity. We passed the Bingo, where some woman howled that she had won the turkey, by glory, every number was covered with a button and she had won the turkey. Overhead, the sun dove behind a cloud and the day went dull. Our shadows disappeared. The arch at the end of the midway drew closer with maddening slowness. ‘Are we home yet?' Ki almost moaned. ‘I want to go home, Mike, please take me home to my mommy.' ‘I will,' I said. ‘Everything's going to be all right.' We were passing the Test Your Strength pole, where the young man with the red hair was putting his shirt back on. He looked at me with stolid dislike the instinctive mistrust of a native for an interloper, per-haps and I realized I knew him, too. He'd have a grandson named Dickie who would, toward the end of the century to which this fair had been dedicated, own the All-Purpose Garage on Route 68. A woman coming out of the quilting booth stopped and pointed at me. At the same moment her upper lip lifted in a dog's snarl. I knew that face, too. From where? Somewhere around town. It didn't matter, and I didn't want to know even if it did. ‘We never should have come here,' Ki moaned. ‘I know how you feel,' I said. ‘But I don't think we had any choice, hon. We ‘ They came out of Freak Alley, perhaps twenty yards ahead. I saw them and stopped. There were seven in all, long-striding men dressed in cutters' clothes, but four didn't matter those four looked faded and white and ghostly. They were sick fellows, maybe dead fellows, and no more dangerous than daguerreotypes. The other three, though, were real. As real as the rest of this place, anyway. The leader was an old man wearing a faded blue Union Army cap. He looked at me with eyes I knew. Eyes I had seen measuring me over the top of an oxygen mask. ‘Mike? Why we stoppin?' ‘It's all right, Ki. Just keep your head down. This is all a dream. You'll wake up tomorrow morning in your own bed.' †Kay.' The jacks spread across the midway hand to hand and boot to boot, blocking our way back to the arch and The Street. Old Blue-Cap was in the middle. The ones on either side of him were much younger, some by maybe as much as half a century. Two of the pale ones, the almost-not-there ones, were standing side-by-side to the old man's right, and I wondered if I could burst through that part of their line. I thought they were no more flesh than the thing which had thumped the insulation of the cellar wall . . . but what if I was wrong? ‘Give her over, son,' the old man said. His voice was reedy and implacable. He held out his hands. It was Max Devore, he had come back, even in death he was seeking custody. Yet it wasn't him. I knew it wasn't. The planes of this man's face were subtly different, the cheeks gaunter, the eyes a brighter blue. ‘Where am I?' I called to him, accenting the last word heavily, and in front of Angelina's booth, the man in the turban (a Hindu who perhaps hailed from Sandusky, Ohio) put down his flute and simply watched. The snake-girls stopped dancing and watched, too, slipping their arms around each other and drawing together for comfort. ‘Where am I, Devore? If our great-grandfathers shit in the same pit, then where am I?' ‘Ain't here to answer your questions. Give her over.' ‘I'll take her, Jared,' one of the younger men-one of those who were really there said. He looked at Devore with a kind of fawning eagerness that sickened me, mostly because I knew who he was: Bill Dean's father. A man who had grown up to be one of the most respected elders in Castle County was all but licking Devore's boots. Don't think too badly of him, Jo whispered. Don't think too badly of any of them. They were very young. ‘You don't need to do nothing,' Devore said. His reedy voice was irritated; Fred Dean looked abashed. ‘He's going to hand her over on his own. And if he don't, we'll take her together.' I looked at the man on the far left, the third of those that seemed totally real, totally there. Was this me? It didn't look like me. There was something in the face that seemed familiar but ‘Hand her over, Irish,' Devore said. ‘Last chance.' ‘No.' Devore nodded as if this was exactly what he had expected. ‘Then we'll take her. This has got to end. Come on, boys.' They started toward me and as they did I realized who the one on the end the one in the caulked treewalker boots and flannel loggers' pants reminded me of: Kenny Auster, whose wolfhound would eat cake 'til it busted. Kenny Auster, whose baby brother had been drowned under the pump by Kenny's father. I looked behind me. The Red-Tops were still playing, Sara was still laughing, shaking her hips with her hands in the sky, and the crowd was still plugging the east end of the midway. That way was no good, anyway. if I went that way, I'd end up raising a little girl in the early years of the twentieth century, trying to make a living by writing penny dreadfuls and dime novels. That might not be so bad . . . but there was a lonely young woman miles and years from here who would miss her. Who might even miss us both. I turned back and saw the jackboys were almost on me. Some of them more here than others, more vital, but all of them dead. All of them damned. I looked at the towhead whose descendants would include Kenny Auster and asked him, ‘What did you do? What in Christ's name did you men do?' He held out his hands. ‘Give her over, Irish. That's all you have to do. You and the woman can have more. All the more you want. She's young, she'll pop em out like watermelon seeds.' I was hypnotized, and they would have taken us if not for Kyra. ‘What's happening?' she screamed against my shirt. ‘Something smells! Something smells so bad! Oh Mike, make it stop!' And I realized I could smell it, too. Spoiled meat and swampgas. Burst tissue and simmering guts. Devore was the most alive of all of them, generating the same crude but powerful magnetism I had felt around his great-grandson, but he was as dead as the rest of them, too: as he neared I could see the tiny bugs which were feeding in his nostrils and the pink corners of his eyes. Everything down here is death, I thought. Didn't my own wife tell me so? They reached out their tenebrous hands, first to touch Ki and then to take her. I backed up a step, looked to my right, and saw more ghosts some coming out of busted windows, some slipping from redbrick chimneys. Holding Kyra in my arms, I ran for the Ghost House. ‘Get him!' Jared Devore yelled, startled. ‘Get him, boys! Get that punk! Goddamnit!' I sprinted up the wooden steps, vaguely aware of something soft rubbing against my cheek Ki's little stuffed dog, still clutched in one of her hands. I wanted to look back and see how close they were getting, but I didn't dare. If I stumbled ‘Hey!' the woman in the ticket booth cawed. She had clouds of gingery hair, makeup that appeared to have been applied with a garden-trowel, and mercifully resembled no one I knew. She was just a carny, just passing through this benighted place. Lucky her. ‘Hey, mister, you gotta buy a ticket!' No time, lady, no time. ‘Stop him!' Devore shouted. ‘He's a goddam punk thief! That ain't his young ‘un he's got! Stop him!' But no one did and I rushed into the darkness of the Ghost House with Ki in my arms. Beyond the entry was a passage so narrow I had to turn sideways to get down it. Phosphorescent eyes glared at us in the gloom. Up ahead was a growing wooden rumble, a loose sound with a clacking chain beneath it. Behind us came the clumsy thunder of caulk-equipped loggers' boots rushing up the stairs outside. The ginger-haired carny was hollering at them now, she was telling them that if they broke anything inside they'd have to give up the goods. ‘You mind me, you damned rubes!' she shouted. ‘That place is for kids, not the likes of you!' The rumble was directly ahead of us. Something was turning. At first I couldn't make out what it was. ‘Put me down, Mike!' Kyra sounded excited. ‘I want to go through by myself!' I set her on her feet, then looked nervously back over my shoulder. The bright light at the entryway was blocked out as they tried to cram in. ‘You asses!' Devore yelled. ‘Not all at the same time! Sweet weeping Jesus!' There was a smack and someone cried out. I faced front just in time to see Kyra dart through the rolling barrel, holding her hands out for balance. Incredibly, she was laughing. I followed, got halfway across, then went down with a thump. ‘Ooops!' Kyra called from the far side, then giggled as I tried to get up, fell again, and was tumbled all the way over. The bandanna fell out of my bib pocket. A bag of horehound candy dropped from another pocket. I tried to look back, to see if they had got themselves sorted out and were coming. When I did, the barrel hurled me through another inadvertent somersault. Now I knew how clothes felt in a dryer. I crawled to the end of the barrel, got up, took Ki's hand, and let her lead us deeper into the Ghost House. We got perhaps ten paces before white bloomed around her like a lily and she screamed. Some animal something that sounded like a huge cat hissed heavily. Adrenaline dumped into my bloodstream and I was about to jerk her backward into my arms again when the hiss came once more. I felt hot air on my ankles, and Ki's dress made that bell-shape around her legs again. This time she laughed instead of screaming. ‘Go, Ki!' I whispered. ‘Fast.' We went on, leaving the steam-vent behind. There was a mirrored corridor where we were reflected first as squat dwarves and then as scrawny ectomorphs with long white vampire features. I had to urge Kyra on again; she wanted to make faces at herself. Behind us, I heard cursing lumberjacks trying to negotiate the barrel. I could hear Devore cursing, too, but he no longer seemed so . . . well, so eminent. There was a sliding-pole that landed us on a big canvas pillow. This made a loud farting noise when we hit it, and Ki laughed until fresh tears spilled down her cheeks, rolling around and kicking her feet in glee. I got my hands under her arms and yanked her up. ‘Don't taggle yer own quartermack,' she said, then laughed again. Her fear seemed to have entirely departed. We went down another narrow corridor. It smelled of the fragrant pine from which it had been constructed. Behind one of these walls, two ‘ghosts' were clanking chains as mechanically as men working on a shoe-factory assembly line, talking about where they were going to take their girls tonight and who was going to bring some ‘red-eye engine,' whatever that was. I could no longer hear anyone behind us. Kyra led the way confidently, one of her little hands holding one of my big ones, pulling me along. When we came to a door painted with glowing flames and marked THIS WAY TO HADES, she pushed through it with no hesitation at all. Here red isinglass topped the passage like a tinted skylight, imparting a rosy glow I thought far too pleasant for Hades. We went on for what felt like a very long time, and I realized I could no longer hear the calliope, the hearty bong! of the Test Your Strength bell, or Sara and the Red-Tops. Nor was that exactly surprising. We must have walked a quarter of a mile. How could any county fair Ghost House be so big? We came to three doors then, one on the left, one on the right, and one set into the end of the corridor. On one a little red tricycle was painted. On the door facing it was my green IBM typewriter. The picture on the door at the end looked older, somehow faded and dowdy. It showed a child's sled. That's Scooter Larribee's, I thought. That's the one Devore stole. A rash of gooseflesh broke out on my arms and back. ‘Well,' Kyra said brightly, ‘here are our toys.' She lifted Strickland, presumably so he could see the red trike. ‘Yeah,' I said. ‘I guess so.' ‘Thank you for taking me away,' she said. ‘Those were scary men but the spookyhouse was fun. Nighty-night. Stricken says nighty-night, too.' It still came out sounding exotic tiu like the Vietnamese word for sublime happiness. Before I could say another word, she had pushed open the door with the trike on it and stepped through. It snapped shut behind her, and as it did I saw the ribbon from her hat. It was hanging out of the bib pocket of the overalls I was wearing. I looked at it a moment, then tried the knob of the door she had just gone through. It wouldn't turn, and when I slapped my hand against the wood it was like slapping some hard and fabulously dense metal. I stepped back, then cocked my head in the direction from which we'd come. There was nothing. Total silence. This is the between-time, I thought. When people talk about ‘slipping through the cracks,' this is what they really mean. This is the place where they really go. You better get going yourself, Jo told me. If you don't want to find yourself trapped here, maybe forever, you better get going yourself. I tried the knob of the door with the typewriter painted on it. It turned easily. Behind it was another narrow corridor more wooden walls and the sweet smell of pine. I didn't want to go in there, something about it made me think of a long coffin, but there was nothing else to do, nowhere else to go. I went, and the door slammed shut behind me. Christ, I thought. I'm in the dark, in a closed-in place . . . it's time for one of Michael Noonan' s world-famous panic attacks. But no bands clamped themselves over my chest, and although my heart-rate was high and my muscles were still jacked on adrenaline, I was under control. Also, I realized, it wasn't entirely dark. I could only see a little, but enough to make out the walls and the plank floor. I wrapped the dark blue ribbon from Ki's hat around my wrist, tucking one end underneath so it wouldn't come loose. Then I began to move forward. I went on for a long time, the corridor turning this way and that, seemingly at random. I felt like a microbe slipping through an intestine. At last I came to a pair of wooden arched doorways. I stood before them, wondering which was the correct choice, and realized I could hear Bunter's bell faintly through the one to my left. I went that way and as I walked, the bell grew steadily louder. At some point the sound of the bell was joined by the mutter of thunder. The autumn cool had left the air and it was hot again stifling. I looked down and saw that the biballs and clodhopper shoes were gone. I was wearing thermal underwear and itchy socks. Twice more I came to choices, and each time I picked the opening through which I could hear Bunter's bell. As I stood before the second pair of doorways, I heard a voice somewhere in the dark say quite clearly: ‘No, the President's wife wasn't hit. That's his blood on her stockings.' I walked on, then stopped when I realized my feet and ankles no longer itched, that my thighs were no longer sweating into the longjohns. I was wearing the Jockey shorts I usually slept in. I looked up and saw I was in my own living room, threading my way carefully around the furniture as you do in the dark, trying like hell not to stub your stupid toe. I could see a little better; faint milky light was coming in through the windows. I reached the counter which separates the living room from the kitchen and looked over it at the waggy-cat clock. It was five past five. I went to the sink and turned on the water. When I reached for a glass I saw I was still wearing the ribbon from Ki's straw hat on my wrist. I unwound it and put it on the counter between the coffee-maker and the kitchen TV. Then I drew myself some cold water, drank it down, and made my way cautiously along the north-wing corridor by the pallid yellow glow of the bathroom nightlight. I peed (you-rinated, I could hear Ki saying), then went into the bedroom. The sheets were rumpled, but the bed didn't have the orgiastic look of the morning after my dream of Sara, Mattie, and Jo. Why would it? I'd gotten out of it and had myself a little sleepwalk. An extraordinarily vivid dream of the Fryeburg Fair. Except that was bullshit, and not just because I had the blue silk ribbon from Ki's hat. None of it had the quality of dreams on waking, where what seemed plausible becomes immediately ridiculous and all the colors both those bright and those ominous fade at once. I raised my hands to my face, cupped them over my nose, and breathed deeply. Pine. When I looked, I even saw a little smear of sap on one pinky finger. I sat on the bed, thought about dictating what I'd just experienced into the Memo-Scriber, then flopped back on the pillows instead. I was too tired. Thunder rumbled. I closed my eyes, began to drift away, and then a scream ripped through the house. It was as sharp as the neck of a broken bottle. I sat up with a yell, clutching at my chest. It was Jo. I had never heard her scream like that in our life together, but I knew who it was, just the same. ‘Stop hurting her!' I shouted into the darkness. ‘Whoever you are, stop hurting her!' She screamed again, as if something with a knife, clamp, or hot poker took a malicious delight in disobeying me. It seemed to come from a distance this time, and her third scream, while just as agonized as the first two, was farther away still. They were diminishing as the little boy's sobbing had diminished. A fourth scream floated out of the dark, then Sara was silent. Breathless, the house breathed around me. Alive in the heat, aware in the faint sound of dawn thunder.

Pricing Options Using Levy Processes And Monte Carlo Finance Essay - Free Essay Example

Sample details Pages: 9 Words: 2574 Downloads: 1 Date added: 2017/06/26 Category Finance Essay Type Analytical essay Did you like this example? The widely known Brownian motion was first introduced in 1828 by a Scottish botanist named Robert Brown. Brown used this concept in order to illustrate an irregularity in patterns of movement by pollen grains suspended in liquid. In 1900, Louis Bachelier considered the Brownian motion as a possible solution to modeling stock market prices. Don’t waste time! Our writers will create an original "Pricing Options Using Levy Processes And Monte Carlo Finance Essay" essay for you Create order As a result, in 1923, Norbert Wiener was the first to give the Brownian Motion a rigorous definition, reconstructing the model. This use of the Brownian theory is often referred to as the Wiener process. Finally, after a series of efforts from a number of scientists, Black and Scholes (1973) introduced the famous Black-Scholes option pricing formula in a paper that remained unpublished. However, later that year, Robert Merton published a follow-up paper that integrated the no-arbitrage condition, generalizing in this way Black-Scholes formula. After Wieners work, Brownian motion was considered, until very recently, the most appropriate process for describing asset returns when operating within a continuous time framework. Nevertheless, a large number of relatively recent studies conclude that Brownian motion may not be the most appropriate process. There are three principal objectives that illustrate this opinion in real life data. First, the volatility of returns is not constant. It changes stochastically, according to time variation. Secondly, asset prices for real data are not continuous, but instead they demonstrate jumps. This, in turn leads to the non-normality of returns. Finally, the returns and their volatilities are not actually independent, rather they often illustrate signs of correlation and sometimes the correlation might even be negative. In particular, Fama (1963) stated that returns are actually more leptokurtic than the normal ones, especially when the holding period is small. In addition, prices on options demonstrate the famous volatility smile and are actually higher than what the Black-Scholes formula predicts. It is also important to note that the Black-Scholes formula assumes normality in log-increments. However, empirical evidence has proved that this is actually false, leading researchers to initiate studies in other ranges of processes. One of the most famous of such family models is the Là ©vy processes. Their greatest advanta ge is that they allow the flexibility of not requiring returns to follow a normal distribution. Finally, the growth of the market has led to the demand of new and more complex financial derivatives for which the Black-Scholes model cannot be used for pricing. As an example, exotic options illustarte this difficulty in pricing very clear, since most times it is impossible to derive a closed-form solution for pricing them. Nonetheless, there are other factors that amplify the complication of pricing an option, as stated in Anyaoku (2005). One such factor, is the early exercise, seen in American options or credit derivatives constructed from a mixture of correlated underlying assets. The path dependent derivatives such as Lookback or Asian options should also be included since their payoff depends on past values of the asset. This kind of options have actually increased in the Over-The-Counter (OTC) market and in order to be traded and hedged, they first need to be priced. The ai m of this paper is to exhibit the use of Là ©vy processes. In particular, we will examine the use of a Variance-Gamma (VG) process (Madan et al. (1998)) in overcoming all the issues of the Brownian motion, mentioned above, when pricing options and in particular American and Asian options. It will turn out that the empirically examined properties of real world data fit a lot better with Là ©vy processes than the Black-Scholes model. Jump-diffusion processes and Là ©vy models have been widely related with option pricing, since they take into account the implied volatility smiles and generally capture all the flaws mentioned above in the Black-Scholes pricing model. The pricing will be employed using Monte Carlo simulation method since it has so far proved an excellent tool for solving problems of higher dimensions. 2. Literature Review 2.1. Construction of Là ©vy processes There is an enormous amount of studies illustrating different option pricing models, as also different processes describing asset prices that were produced as an alternative to the flawed Black-Scholes model. Là ©vy process was one of the most widespread alternatives and researchers up until now are studying the different versions of it. In particular, the first studies about the Là ©vy process go back to the late 20s but its final structure was gradually discovered by a number of researchers such as De Finetti, Kolmogorov, Là ©vy, Khintchine and Ità ´. Broadly speaking, a Là ©vy process is a stochastic process in continuous time with independent and stationary increments, similar to the independent and identically distributed improvement of discrete monitoring. The two most famous Là ©vy processes are, the Brownian motion with drift, used in the Black-Scholes model (1973) and the compound Poisson process which underlies Mertons (1976) jump diffusion model. Carr and Wu (2004) mentioned in their paper about time-changed Là ©vy processes that a pure jump Là ©vy process generates non-normal innovations and in order to capture the stochastic volatility, they applied a stochastic time change to the process. In addition, they mentioned that in order for the correlation between returns and their volatilities to appear, they had to allow improvements in the process to be correlated with improvements in the random clock on which it is run. In the case where the later correlation becomes negative, it means that when the Là ©vy process falls the clock has a faster running trend. This is what detains the leverage effect described in Black (1976). There is a huge variety of different types of Là ©vy processes that are used in pricing options and researchers share separate opinions about which one is actually more suitable. This variety of opinions was clearly illustrated by Carr and Wu (2004). One sort consists of those who believe that compound Poisson processes are appropriate for fitting jumps as it was first mentioned by Merton (1976). Similar to this was Hestons (1993) idea in using a mean reverting square root process when modeling stochastic volatility. Among those who undertook the same research path were Andersen et al. (2002), Bates (2000) and Pan (2002). The second sort considers general jump structures which allow an infinite number of jumps to arise within a finite time interval. One of the most commonly used models in this strand is the inverse Gaussian model, introduced by Barndorff-Nielsen (1998), as well as the Variance-Gamma (VG) model, introduced by Madan et al. (1998). This strand basically supports the use of infinite-activity process when modeling returns, which leads to the recognition of stochastic volatility. The best elements of the two strands mentioned above are suitably combined in time-changed Là ©vy processes, creating an even better fit. In particular, the time-changed framework relaxes the a ffine requirement and allows greater generality for the jump structure. In addition, it allows volatility changes to be correlated arbitrarily with asset returns. This leads to the privilege of attaining both the leverage effect missing from the Black-Scholes model and the high jump activity as seen in Carr and Wu (2004). 2.2. Recent work on pricing using Là ©vy Processes Option pricing is an issue that concerned researchers for decades and it will likely continue to be an issue for years to come. The methodology used for observing pricing behavior varies largely, depending on the type of options and process you are dealing with. Most of the times, pricing of options requires numerical integration or solving a partial differential equation (PDE). However, this is not always feasible. When the dimension of the problem is large, both numerical integrals and solving PDEs become hard to implement since formulas become intractable and a large amount of accuracy is lost (Jia (2009)). This is where estimation methods are introduced, in order to offer more accurate results. Several groups of numerical methods, implemented in recent studies, exist for analyzing option pricing. The most commonly used are the Monte Carlo simulations and Fast Fourier Transforms (FFT). Monte Carlo simulation, in particular, can be applied in evaluating options that contain multi ple sources of ambiguity or obscured characteristics. However, a number of other differing analytical approximations are used, as well as derivations of integral equations. One approach was that of Madan et al. (1998) who examined a stochastic process, in which financial information arrived via jumps. In their study, they applied a high-activity process with infinite small jumps, combining them with the lower-frequency large jumps. Following their work, Carr and Wu (2003) examined the necessity of a diffusion component, when using high-activity pure jump processes. However, they did not manage to reach an exact conclusion since often jump processes in the limit imitate the performance of a diffusion process. Nonetheless, they realized that when pricing short-term index options at-the-money, a diffusion component offers some contribution. Benhamou (2000), in his effort to model the smile effect, implemented both Fourier and Laplace transforms in a semi-parametric method. The on ly assumption required was that Là ©vy processes are appropriate in modeling underlying price processes. However, no other constraints were employed on the price process. In this way, he managed to broaden the Black-Scholes model to a variety of Là ©vy processes, due to the fact that the latter includes both continuous time diffusion and jump process. Another approach was that of Lord et al. (2007). They examined the pricing of early-exercise options by introducing a novel quadrature-based method which mainly relies on Fast-Fourier transformations called the Convolution method. Their work was a combination of the recent quadrature pricing methods of Andricopoulos et al. (2003) and OSullivan (2005) and the Fourier transformation methods initiated by Carr and Madan (1999), Raible (2000) and Lewis (2001). The main idea of the procedure applied was to reformulate the commonly used risk-neutral valuation formula on the basis that it forms a convolution. The Convolution method is the n used for pricing American and Bermudan options. In order to implement this method, they had to impose only one restriction, basically that of a known conditional characteristic function for the underlying asset. However, since the method was applied within an exponential Là ©vy framework, which includes the exponential affine jump-diffusion models, the constraint for a known conditional characteristic function was fulfilled. In the report, the flexibility of choosing the asset price process within a range of jump processes was illustrated in numerical examples by examining three different processes; namely, the Geometric Brownian Motion (GBM), the VG and the CGMY (Carr et al.(2002)). Finally, an apparent example on the use of Monte Carlo simulation in pricing exotic options by making use of general pricing techniques for vanilla options is given by Schoutens and Symens (2002). A thorough observation should be made of their work, since this report will use the same procedure in pricing American and Asian options. The processes exploited when pricing the options were the VG process, the Normal Inverse Gaussian (NIG) process and the Meixner process, which were then used to implement a Là ©vy Stochastic Volatility (Là ©vy-SV) model. Broadly speaking, in a stochastic volatility model, the time of the process becomes stochastic. This means that time is running slow when we are at times of low volatility and time is running fast when we are at times of high volatility. As a rate of time change, they used the Cox-Ingersoll-Ross (CIR) model and they calibrated the Là ©vy-SV model to fit their data set, which was completed with mid-prices of a set of European call options on the SP 500 index. The calibration produced the risk-neutral parameters for each model, on which they carried out simulations and obtained the option prices for all proposed models. Finally, the use of the technique of control variates was made in order to decrease the standard error of the simulations to a minimum. As a result, they realized that although in the Black-Scholes framework, prices of exotic options depend highly on the volatility parameter chosen, which is not apparent; in the Là ©vy-SV model, prices are almost equal. This is what led them to the conclusion that pricing exotic options on the Là ©vy-SV model is more reliable than the Black-Scholes model. 3. Data Requirements and Methodologies to be used Following the procedure above by Schoutens and Symens (2002), we will price an American option and an exotic option, specifically an Asian fixed strike call option with arithmetic average, using Monte Carlo simulations. Generally, there are two types of research approaches: quantitative and qualitative. The main difference of the two is that the first is objective in nature, i.e. it is not influenced, whilst the second approach is subjective in nature, i.e. it is influenced. The data we would use to implement our model will be FTSE 100 index prices for a 5 year period. The payoff of an American and an Asian option are given in the following way. American Option: Where is the stopping time representing the optimal stopping time and is the payoff of the American contract to be priced. Asian Fixed Strike Call Option: Let = average of the asset price over Assume stock prices are recorded every periods from time to time , then there are periods over . The payoff of the Asian fixed strike call option is given by , where is the strike price. By using a VG model, we will calibrate model prices in order to try and match them to market prices by minimizing the least squared error of their differences. In particular, for computing the average absolute error we would use the following formula The procedure begins by simulating different paths for our stock prices process (in our case the VG process) and then for each path evaluate the payoff function for , where is the number of options in our data set. From that, we calculate the Monte Carlo estimate of the expected payoff as The above estimate is used to discount the final option price, i.e. . The standard error of this estimate is then required, which is given by: Generally, it is observed that in order to decrease the standard error of the estimate, you need to increase the number of simulations. However, one should note that when increasing the number of simulations, the speed of the pr ocedure decreases. We continue by simulating our VG process up to time The final step includes the rescaling of our path based on the path of the stochastic business time of our choice and then inserting it in the formula for the behavior of the stock price. Finally, we should note that the stochastic time we chose to use is the Cox-Ingersoll-Ross (CIR (1985a/b)) model. 4. Conclusion In this report, our aim is to illustrate a way of pricing American and Asian options that detain all key aspects on real world financial securities; mainly, jumps, stochastic volatility and the leverage effect. By using a VG process, we obtain a framework that allows jumps and with the help of the CIR model, as the stochastic time, we allow for stochastic volatility to be introduced. Finally, the leverage effect is captured through the correlation between the VG innovation and the time change. Generally, the Black-Scholes model will always remain as a point of reference against all other models or extensions pioneered and it will continue to be seen as a paradigm of option pricing regardless of the amount of research that has occurred, proving the opposite. However, recent studies have been evident of the flaws of the Black-Scholes model when applied to the real world framework. In addition, it has been proven that Là ©vy processes can be considered as the most recent effective fit to the actual market. Nevertheless, in future research everything is possible to revolutionize.