Black-Scholes Formulae for Asian Options in Local Volatility Models
University of Bologna - Department of Statistics
University of Padua - Department of Pure and Applied Mathematics
University of Bologna - Department of Mathematics
July 29, 2011
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.
Number of Pages in PDF File: 29
Keywords: Asian option, analytic approximation, hypoelliptic PDE
JEL Classification: G00, G13working papers series
Date posted: July 31, 2011 ; Last revised: December 12, 2011
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