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

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Modeling Uncertainty in Banking Networks,totic behavior of the implied volatility in special models without moment explosions. The list of such models includes the displaced diffusion model, the constant elasticity of variance model, the finite moment log-stable model of P. Carr and L. Wu, and SV1 and SV2 models developed by L.C.G. Rogers and L.A.M. Veraart.

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Implied Volatility in Models Without Moment Explosions,totic behavior of the implied volatility in special models without moment explosions. The list of such models includes the displaced diffusion model, the constant elasticity of variance model, the finite moment log-stable model of P. Carr and L. Wu, and SV1 and SV2 models developed by L.C.G. Rogers and L.A.M. Veraart.

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Asymptotic Analysis of Mixing Distributions,ory of hypergeometric functions, and some methods from complex analysis. Dufresne’s recurrence formula, which allows one to navigate between the Hull-White models with different values of the model parameters, is also covered in Chap. 5.

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Asymptotic Analysis of Stock Price Distributions,els established in Chap. .. Extensions of the asymptotic formulas for the stock price density to the case of the correlated Heston and Stein-Stein models are also presented. The asymptotic behavior of the stock price density in the correlated Hull-White model remains a mystery.

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Asymptotic Analysis of Option Pricing Functions,k-Scholes model. This celebrated model is discussed in the present chapter and an analytical proof of the Black-Scholes formula is given. Moreover, sharp asymptotic formulas are obtained for call pricing functions in the Hull-White, Stein-Stein, and Heston models.

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