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February 2015 A family of density expansions for Lévy-type processes
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
Ann. Appl. Probab. 25(1): 235-267 (February 2015). DOI: 10.1214/13-AAP994

Abstract

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale subject to default. This class of models allows for local volatility, local default intensity and a locally dependent Lévy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci and Riga [SIAM J. Financial Math. 4 (2013) 265–296], we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and defaultable bond prices. For the density expansion, we also provide error bounds for the truncated asymptotic series. Our method is numerically efficient; approximate transition densities and European option prices are computed via Fourier transforms; approximate bond prices are computed as finite series. Additionally, as in Pagliarani, Pascucci and Riga (2013), for models with Gaussian-type jumps, approximate option prices can be computed in closed form. Sample Mathematica code is provided.

Citation

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Matthew Lorig. Stefano Pagliarani. Andrea Pascucci. "A family of density expansions for Lévy-type processes." Ann. Appl. Probab. 25 (1) 235 - 267, February 2015. https://doi.org/10.1214/13-AAP994

Information

Published: February 2015
First available in Project Euclid: 16 December 2014

zbMATH: 1329.60122
MathSciNet: MR3297772
Digital Object Identifier: 10.1214/13-AAP994

Subjects:
Primary: 35R09, 60G99, 91G20, 91G80

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 1 • February 2015
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