Pricing American Options Fitting the Smile

M. A. H. Dempster and D. G. Richards

Mathematical Finance, 2000, vol. 10, issue 2, 157-177

Abstract: This paper is a compendium of results—theoretical and computational—from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one‐factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast—lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile.

Date: 2000
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