Local Stochastic Volatility with Jumps: Analytical Approximations

Int. J. Theor. Appl. Finan. 16, 1350050, 2013, DOI: org/10.1142/S0219024913500507

38 Pages Posted: 5 Jun 2012 Last revised: 19 Nov 2016

Stefano Pagliarani

DEAMS, Università di Trieste

Andrea Pascucci

University of Bologna - Department of Mathematics

Date Written: August 16, 2013

Abstract

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

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

JEL Classification: G13

Suggested Citation

Pagliarani, Stefano and Pascucci, Andrea, Local Stochastic Volatility with Jumps: Analytical Approximations (August 16, 2013). Int. J. Theor. Appl. Finan. 16, 1350050, 2013, DOI: org/10.1142/S0219024913500507. Available at SSRN: https://ssrn.com/abstract=2077394 or http://dx.doi.org/10.2139/ssrn.2077394

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

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