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|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
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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.
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9319, University Library of Munich, Germany.
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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.
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- Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, 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.
- Sam Howison, 2005. "Matched asymptotic expansions in financial engineering," OFRC Working Papers Series 2005mf01, Oxford Financial Research Centre.
- 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. Full references (including those not matched with items on IDEAS)
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