Expansion formulae for local Lévy models
We propose a novel method for the analytical approximation in local volatility models with Lèvy jumps. In the case of Gaussian jumps, we provide an explicit approximation of the transition density of the underlying process by a heat kernel expansion: the approximation is derived in two ways, using PIDE techniques and working in the Fourier space. Our second and main result is an expansion of the characteristic function for a local volatility model with general Lévy jumps. Combined with standard Fourier methods, such an expansion allows to obtain efficient and accurate pricing formulae. Numerical tests confirm the effectiveness of the method.
|Date of creation:||20 Oct 2011|
|Date of revision:|
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Web page: https://mpra.ub.uni-muenchen.de
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- E. Benhamou & E. Gobet & M. Miri, 2010. "Expansion Formulas For European Options In A Local Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 603-634.
- Guoping Xu & Harry Zheng, 2010. "Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method," Papers 1003.1848, arXiv.org.
- Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
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- Xu, Guoping & Zheng, Harry, 2010. "Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 415-422, December.
- Fang, Fang & Oosterlee, Kees, 2008.
"A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions,"
7700, University Library of Munich, Germany.
- Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
- E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
- Paolo Foschi & Stefano Pagliarani & Andrea Pascucci, 2011. "Black-Scholes formulae for Asian options in local volatility models," Quaderni di Dipartimento 7, Department of Statistics, University of Bologna.
- Rama Cont & Nicolas Lantos & Olivier Pironneau, 2011. "A reduced basis for option pricing," Post-Print hal-00522410, HAL.
- Sam Howison, 2005. "Matched asymptotic expansions in financial engineering," OFRC Working Papers Series 2005mf01, Oxford Financial Research Centre.
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