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The Fourier Approach of the American Option Pricing Under Jump-diffusion Processes

Author: LiPeiLin
Tutor: LiuShaoYue
School: Xiangtan University
Course: Probability Theory and Mathematical Statistics
Keywords: American Option Jump - diffusion process Fourier transform of the extended Cauchy residue theorem Iterative method
CLC: F830.9
Type: Master's thesis
Year: 2010
Downloads: 71
Quote: 0
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Abstract


The American Option options products are the most widely traded in the financial markets, which studied the most is that stock options. Empirical studies have shown that the stock prices on the financial markets is not a simple geometric Brownian motion, but showed a leptokurtic distribution characteristics can be used to jump - diffusion model to describe more general. Jump - diffusion process for pricing American options are options in theory and difficult problems, the biggest difficulty lies in the non-locality of the problem of pricing American options can advance the implementation of the characteristics caused by the jump integral equation, use up method is based on the finite element method for variational inequalities. And difficult due to the complex structure of such methods, computer programming, the article attempts to use the extended Fourier transform method of pricing American put option under the jump - diffusion process, in order to provide the alternative to solve such problems perspectives and ideas. The first chapter briefly jump - diffusion process Research of the American option pricing, a comprehensive comparison of the current use of pricing methods, and then based on this method, and finally introduce the main research job. The second chapter is the basis of the subsequent chapters, in this chapter, the paper first introduces the no-arbitrage pricing of financial mathematics, the martingale, Ito Lemma and other important concepts and formulas, and then specifically introduced the BSM the basic model and jump - diffusion model, On this basis, this paper intends to solve the free boundary problem of American option again. After the introduction of these mathematical models, the paper goes on to explain the expansion of the Fourier transform method - this is the main method used in this article, as well as the inside of the complex function of the Cauchy residue theorem and weekly line integral knowledge. The third chapter is the main sections of this paper, another Fourier transform method to solve the American option pricing problem in this chapter, we first compared, and then gives the key assumptions used in the key assumptions , the paper uses the extended Fourier transform method for pricing of American put option under the jump - diffusion process and to use the weeklies transform Transform Solution of the Cauchy principal value integral form, and finally the integral equivalence transformation, in order to explain and numerical. Chapter is to verify the correctness of the key assumptions and results of Chapter III of this paper numerical implementation section, the first iteration method to determine the free boundary, then the value of the options, last compared numerical implementation results, and gives the conclusion.

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market
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