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Numerical Methods for American Options Pricing

Author: TangYaoZong
Tutor: JinChaoZuo
School: Chongqing University
Course: Computational Mathematics
Keywords: B-S model American Option Finite difference method Adaptive mesh model Meshless method
CLC: F224
Type: Master's thesis
Year: 2008
Downloads: 359
Quote: 0
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Abstract


The option is one of the most important financial derivatives as a financial innovation tools , prevention and risk-averse , and the speculative plays a very important role . Reasonable mathematical model to determine the price of the option became investors Application Option key issues to avoid financial risks in the financial sector , the option pricing problems become an important area of theoretical and applied research . For the European option , Black Sholes already given in the analytical form of the pricing formula . American option pricing , however , is not the existence of such analytical formulas also can not obtain the exact solution . Real world, most options exchange transactions for the American Option . Therefore , the development of a wide variety of computing the value of the American option price method has important theoretical and practical significance . The mathematical model of the American option pricing problem generally can be summed up as a free boundary problem . The introduction part of this article made ??a broad review of financial derivatives pricing theory ; described in the second part of the derivative securities prices obey the Black-Scholes partial differential equations ; third part of the traditional binary tree , the the trigeminal tree model improved . Encryption tree diagram grid that is , in the appropriate area , while the other region is not change in order to eliminate the problem of the presence of the nonlinear error in the rough tree FIG grid , to better reflect the actual situation , such that only a very small increase computation can achieve the effect of the original need to achieve higher density tree diagram calculation . The fourth part is based on the BS differential equations , finite-difference method parameter setting method to improve , and a certain combination of traditional implicit finite difference method and finite difference method of extrapolation to obtain better results . The fifth part of the standard form of a number of underlying asset European option derived , and derived using the method of fundamental solutions (MFS method ) based on the convection-diffusion differential equations to solve partial differential equations in standard form . MFS method taking into account the characteristics of American options and features of the MFS method to solving American options . The third, fourth, five each part with a numerical example to verify the effectiveness and practicality of the chapter .

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CLC: > Economic > Economic planning and management > Economic calculation, economic and mathematical methods > Economic and mathematical methods
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