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Description:
Artur Sepp

Abstract
This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jumpdiffusions. We provide a broad description of the issues and a detailed summary of the main points and features of the models proposed. First, we consider a wide class of affine jump-diffusions proposed for the asset price dynamics: jump-diffusions, diffusions with stochastic volatility, jump-diffusions with stochastic volatility, and jump-diffusions with stochastic volatility and jump intensity. Next we apply the Fourier transform for solving the problem of European option pricing under these price processes. We present two solution methods: the characteristic formula and the Black- Scholes-style formula. Finally, we discuss numerical implementation of pricing formulas and apply the considered processes for modeling the DAX options volatility surface.