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Adjoint Expansions in Local Lévy Models

Pagliarani S., Pascucci, A., Riga C., SIAM J. Finan. Math., 4(1), 265–296. DOI:10.1137/110858732

36 Pages Posted: 4 Oct 2011 Last revised: 17 Nov 2016

Stefano Pagliarani

DEAMS, Università di Trieste

Andrea Pascucci

University of Bologna - Department of Mathematics

Candia Riga

Scuola Normale Superiore di Pisa; Sciences mathématiques de Paris Centre - Spécialité: Probabilités; University of Bologna - Department of Mathematics

Date Written: October 20, 2011

Abstract

We propose a novel method for the analytical approximation in local volatility models with Lévy jumps. The main result is an expansion of the characteristic function in a local Lévy model, which is worked out in the Fourier space by considering the adjoint formulation of the pricing problem. Combined with standard Fourier methods, our result provides efficient and accurate pricing formulae. In the case of Gaussian jumps, we also derive an explicit approximation of the transition density of the underlying process by a heat kernel expansion: the approximation is obtained in two ways, using PIDE techniques and working in the Fourier space. Numerical tests confirm the effectiveness of the method.

Keywords: Lévy process, local volatility, analytical approximation, partial integro-differential equation, Fourier methods

JEL Classification: G00, G13

Suggested Citation

Pagliarani, Stefano and Pascucci, Andrea and Riga, Candia, Adjoint Expansions in Local Lévy Models (October 20, 2011). Pagliarani S., Pascucci, A., Riga C., SIAM J. Finan. Math., 4(1), 265–296. DOI:10.1137/110858732. Available at SSRN: https://ssrn.com/abstract=1937149 or http://dx.doi.org/10.2139/ssrn.1937149

Stefano Pagliarani

DEAMS, Università di Trieste ( email )

Via Valerio n. 4/1
Trieste
Italy

HOME PAGE: http://www.cmap.polytechnique.fr/~pagliarani/

Andrea Pascucci (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

HOME PAGE: http://www.dm.unibo.it/~pascucci

Candia Riga

Scuola Normale Superiore di Pisa ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Sciences mathématiques de Paris Centre - Spécialité: Probabilités

175 Rue du Chevaleret
Paris, 75013
France

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

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