TY - BOOK ID - 7987618 TI - Analytically Tractable Stochastic Stock Price Models PY - 2012 SN - 3642433863 3642312136 9786613943408 3642312144 1283630958 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Capital assets pricing model. KW - Global analysis (Mathematics). KW - Stocks -- Prices -- Mathematical models. KW - Business & Economics KW - Economic Theory KW - Stock price forecasting KW - Stock price indexes. KW - Mathematical models. KW - Averages, Stock KW - Indexes, Stock KW - Stock averages KW - Stock indexes KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Approximation theory. KW - Applied mathematics. KW - Engineering mathematics. KW - Economics, Mathematical. KW - Probabilities. KW - Quantitative Finance. KW - Analysis. KW - Probability Theory and Stochastic Processes. KW - Approximations and Expansions. KW - Applications of Mathematics. KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Economics KW - Mathematical economics KW - Econometrics KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Theory of approximation KW - Functional analysis KW - Functions KW - Polynomials KW - Chebyshev systems KW - 517.1 Mathematical analysis KW - Math KW - Science KW - Methodology KW - Price indexes KW - Finance. KW - Distribution (Probability theory. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Funding KW - Funds KW - Currency question KW - Economics, Mathematical . KW - Social sciences KW - Mathematics in Business, Economics and Finance. KW - Probability Theory. UR - https://www.unicat.be/uniCat?func=search&query=sysid:7987618 AB - 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. ER -