Approximations for Asian options in local volatility models

Authors:
Paolo Foschi;Stefano Pagliarani;Andrea Pascucci
Affiliations:
Dipartimento di Scienze Statistiche "Paolo Fortunati", Universití di Bologna, Via Belle Arti 41, 40126 Bologna, Italy;Dipartimento di Matematica, Universití di Padova, Via Trieste 63, 35121 Padova, Italy;Dipartimento di Matematica, Universití di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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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.