Titlebook: Applications of Fourier Transform to Smile Modeling; Theory and Implement Jianwei Zhu Book 2010Latest edition Springer-Verlag Berlin Heidel

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Stochastic Interest Models,s can be incorporated into a pricing formula for European-style stock options. To this end, we focus on only three typical one-factor short rate models, namely, the Vasicek model (1977), the CIR model (1985) and the Longstaff model (1989), which are again specified by a mean-reverting Ornstein-Uhlen

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Poisson Jumps,a based on a stock price process generated by a mixture of a Brownian motion and a Poisson process. This mixed process is also called the jump-diffusion process. The requirement for a jump component in a stock price process is intuitive, and supported by the big crashes in stock markets: The Black M

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,Lévy Jumps, be regarded as two special cases of Lévy process, and have only finite activity in a finite time interval. In this chapter, we only consider Lévy processes with infinity activity in a finite time interval. With respect to jump event modeling in finance, compound Poisson jumps discussed in Chapter 7

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Exotic Options with Stochastic Volatilities,., path-dependent options). There is a long list of financial derivatives belonging to this class: barrier options, Asian options, correlation options, spread options, exchange options, clique options etc. Most of them are generated in the course of the expansion of the financial derivative business

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Libor Market Model with Stochastic Volatilities,icing model for interest rate derivatives. Since LMM is based on a series of lognormal dynamics, the methods for building up the smile models, particularly with stochastic volatilities, can be adopted from the previous chapters. After a brief introduction to interest derivative markets in Section 11

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Jesper Larsson Tr?ff,Robert A. vande Geijnrate modeling are two ideal candidate processes for stochastic volatilities. Heston (1993) specified stochastic variances with a mean-reverting square root process and derived a pioneering pricing formula for options by using CFs. Stochastic volatility model with a mean-reverting Ornstein-Uhlenbeck

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