Titlebook: Analytically Tractable Stochastic Stock Price Models; Archil Gulisashvili Book 2012 Springer-Verlag Berlin Heidelberg 2012 91Gxx, 91G80, 9

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Asymptotic Analysis of Mixing Distributions,etric Brownian motions, Ornstein-Uhlenbeck processes, and CIR-processes. Sharp asymptotic formulas with relative error estimates are established for these densities, using various combinations of techniques and tools. The proofs employ a Tauberian theorem for the two-sided Laplace transform, the the

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Asymptotic Analysis of Stock Price Distributions, estimates for stock price densities in the uncorrelated Hull-White, Stein-Stein, and Heston models due to E.M. Stein and the author are presented in this chapter. The proofs use the asymptotic formulas for mixing distributions and the Abelian theorem for the integral transforms with log-normal kern

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Regularly Varying Functions and Pareto-Type Distributions,ies. Chapter 7 provides a short overview of the theory of regularly varying functions. In addition, the chapter discusses Pareto type distributions, which are distributions with regularly varying tails. A new notion of weak Pareto type functions is introduced and studied. A function is of a weak Par

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Asymptotic Analysis of Implied Volatility,udied standard deviations of asset returns, which are implied in actual call option prices when investors price options according to the Black-Scholes model. Chapter 9 mainly is concerned with the asymptotics of the implied volatility at extreme strikes. It presents sharp model-free asymptotic formu

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https://doi.org/10.1007/978-3-642-31214-491Gxx, 91G80, 91B25, 91G20; asymptotic formulas; implied volatilities; option pricing functions; stochas

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