Mathematical Modeling and Methods of Option Pricing

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World Scientific, 2005 - Science - 329 pages
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From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
 

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Contents

Risk Management and Financial Derivatives
1
ArbitrageFree Principle
9
Binomial Tree Methods Discrete Models of Option Pricing
25
Brownian Motion and I to Formula
55
European Option Pricing BlackScholes Formula
73
nite Difference Method
100
American Option Pricing and Optimal Exercise Strategy
113
MultiAsset Option Pricing
201
PathDependent Options
247
Implied Volatility
311
Bibliography
323
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