Pricing American Options Fitting the Smile

21 Pages Posted: 17 Mar 2001 Last revised: 5 Aug 2018

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

Darren G. Richards

University of Cambridge - Judge Business School

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.

Suggested Citation

Dempster, M. A. H. and Richards, Darren G., Pricing American Options Fitting the Smile. Mathematical Finance, Vol. 10, No. 2, April 2000. Available at SSRN: https://ssrn.com/abstract=242886

M. A. H. Dempster (Contact Author)

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

Darren G. Richards

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom
+44 (0) 1223 339648 (Phone)
+44 (0) 1223 339652 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
4
Abstract Views
943
PlumX Metrics