Expansion formulae for local Lévy models

Pagliarani, Stefano ; Pascucci, Andrea ; Riga, Candia (2011) Expansion formulae for local Lévy models. [Preprint]
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Abstract

We propose a novel method for the analytical approximation in local volatility models with Lévy 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.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Pagliarani, Stefano
Pascucci, Andrea
Riga, Candia
Keywords
Lévy process, local volatility, asymptotic expansion, partial-integro differential equation, Fourier methods
Subjects
DOI
Deposit date
09 Nov 2011 08:50
Last modified
20 Dec 2011 11:53
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