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- W932559635 abstract "This paper gives a description of how Levy processes are utilized in order to establish a more accurate model of the financial market than the standard Black-Scholes model. The Levy process that is discussed in this paper uses the Normal Inverse Gaussian (NIG) distribution. Stochastic volatility is also addressed with the help of CIRprocesses. The end result is a comparison between the standard BlackScholes model, the model with a NIG distribution and a Black-Scholes model with stochastic volatility. The comparison is done with respect to pricing and measurements of risk in the form of estimating American options and the greek delta. To accomplish this the Black-Scholes model is formulated following a discussion about its inconsistencies with the real financial market. Then Levy processes and CIR-processes are established followed by a section about how to simulate these processes and a section about estimating American options and greeks. Acknowledgements. I would first like to thank my supervisor Professor Maciej Klimek for his encouragement and support. He has consistently been available to discuss the subject and scope of the thesis. 1. the black-scholes model The Black-Scholes model is a mathematical interpretation of a financial market consisting of stocks, bonds and derivatives. The bond is said to be risk-free while the stock has a risk component. This market is assumed to be free of arbitrage, meaning a trader can not make an initial investment of zero that later leads to a profit with probability 1 hence with no risk involved. In the Black-Scholes model the stock has the following stochastic dynamics: (1) dSt = μStdt+ σStdBt where μ is the expected rate of return of the stock and σ is the volatility i.e standard deviation of returns of the stock. If a stock is assumed to pay dividend with dividend yield q, then (1) becomes (2) dSt = (μ− q)Stdt+ σStdBt 1" @default.
- W932559635 created "2016-06-24" @default.
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- W932559635 date "2015-01-01" @default.
- W932559635 modified "2023-09-27" @default.
- W932559635 title "Pricing American Options using Lévy Processes and Monte Carlo Simulations" @default.
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