Stefano, Pagliarani and Pascucci, Andrea and Candia, Riga (2011): Adjoint expansions in local Lévy models.
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Abstract
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.
Item Type:  MPRA Paper 

Original Title:  Adjoint expansions in local Lévy models 
English Title:  Adjoint expansions in local Lévy models 
Language:  English 
Keywords:  Lévy process, local volatility, asymptotic expansion, partialintegro differential equation, Fourier methods 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  35788 
Depositing User:  Andrea Pascucci 
Date Deposited:  09. Jan 2012 04:41 
Last Modified:  15. Feb 2013 22:50 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/35788 
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Expansion formulae for local Lévy models. (deposited 07. Nov 2011 18:12)
 Adjoint expansions in local Lévy models. (deposited 09. Jan 2012 04:41) [Currently Displayed]