Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform
Kangro, R., Parna, K., and Sepp, A., (2004), "Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform", Acta et Commentationes Universitatis Tartuensis de Mathematica 8, 123-133
30 Pages Posted: 31 May 2009 Last revised: 18 Feb 2014
Date Written: September 7, 2003
This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jump-diffusions. 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.
Keywords: stochastic volatility, jump-diffusion processes, volatility smile, option pricing, characteristic function, Fourier transform, DAX volatility surface
JEL Classification: C, G
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