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＜電子ブック＞
Analytically Tractable Stochastic Stock Price Models / by Archil Gulisashvili
(Springer Finance. ISSN:21950687)

版	1st ed. 2012.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2012
本文言語	英語
大きさ	XVIII, 362 p : online resource
著者標目	*Gulisashvili, Archil author SpringerLink (Online service)
件　名	LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Mathematical analysis LCSH:Probabilities LCSH:Approximation theory LCSH:Mathematics FREE:Mathematics in Business, Economics and Finance FREE:Analysis FREE:Probability Theory FREE:Approximations and Expansions FREE:Applications of Mathematics
一般注記	Preface -- Aknowledgements -- 1.Volatility Processes -- 2.Stock Price Models with Stochastic Volatility -- 3.Realized Volatility and Mixing Distributions -- 4.Integral Transforms of Distribution Densities -- 5.Asymptotic Analysis of Mixing Distributions -- 6.Asymptotic Analysis of Stock Price Distributions -- 7.Regularly Varying Functions and Pareto Type Distributions -- 8.Asymptotic Analysis of Option Pricing Functions -- 9.Asymptotic Analysis of Implied Volatility -- 10.More Formulas for Implied Volatility -- 11.Implied Volatility in Models Without Moment Explosions -- Bibliography -- Index Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory HTTP:URL=https://doi.org/10.1007/978-3-642-31214-4

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