Approximations for Asian Options in Local Volatility Models

Foschi P., Pagliarani S., Pascucci A., Journal of Computational and Applied Mathematics, Volume 237, Issue 1, 1 January 2013, Pages 442-459. DOI:10.1016/j.cam.2012.06.015

30 Pages Posted: 31 Jul 2011 Last revised: 17 Nov 2016

Paolo Foschi

University of Bologna - Department of Statistics

Stefano Pagliarani

DEAMS, Università di Trieste

Andrea Pascucci

University of Bologna - Department of Mathematics

Date Written: February 7, 2012

Abstract

We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat kernel expansion method in the framework of hypoelliptic, not uniformly parabolic, partial differential equations. The Mathematica notebook with the implementation of the formulae is freely available in the authors' website.

Keywords: Asian option, analytic approximation, hypoelliptic PDE

JEL Classification: G00, G13

Suggested Citation

Paolo Foschi and Pagliarani, Stefano and Pascucci, Andrea, Approximations for Asian Options in Local Volatility Models (February 7, 2012). Foschi P., Pagliarani S., Pascucci A., Journal of Computational and Applied Mathematics, Volume 237, Issue 1, 1 January 2013, Pages 442-459. DOI:10.1016/j.cam.2012.06.015. Available at SSRN: https://ssrn.com/abstract=1898992 or http://dx.doi.org/10.2139/ssrn.1898992

Paolo Foschi

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

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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