Open AccessPricing European-style options under jump diffusion processes with stochastic volatility: applications of Fourier transform
Author(s) -
Raul Kangro,
Kalev Pärna,
Artur Sepp
Publication year - 2004
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2004.08.08
Subject(s) - stochastic volatility , jump diffusion , volatility smile , implied volatility , fourier transform , valuation of options , mathematics , black–scholes model , sabr volatility model , heston model , jump , volatility (finance) , econometrics , mathematical economics , mathematical analysis , physics , quantum mechanics
We develop a general methodology for pricing European-style options under various stochastic processes via the Fourier transform. We generalize previous work in this field and present two approaches for solving the pricing problem: the characteristic formula which is an extension of Lewis (2001) work, and the Black-Scholes-style formula which is an extension and generalization of previous works by Heston (1993) and Bates (1996). We show how to apply our formulas for two types of asset price dynamics: 1) stochastic volatility models with price jumps at a stochastic jump intensity rate, 2) stochastic volatility models with price and volatility jumps. Convergence properties of Fourier integrals arising from both approaches are studied.