Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

28 Pages Posted: 7 Nov 2010 Last revised: 23 Jun 2011

See all articles by Pierre Del Moral

Pierre Del Moral

INRIA Bordeaux-Sud Ouest; University of Bordeaux - University of Bordeaux 1

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Sylvain Rubenthaler

Université de Nice Sophia Antipolis

Date Written: October 30, 2010

Abstract

It can be shown that when the payoff function is convex and decreasing (respectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies.

Keywords: American Option, Simulation, Exercise Region, Snell Envelope

Suggested Citation

Del Moral, Pierre and Remillard, Bruno and Rubenthaler, Sylvain, Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity (October 30, 2010). Available at SSRN: https://ssrn.com/abstract=1703906 or http://dx.doi.org/10.2139/ssrn.1703906

Pierre Del Moral

INRIA Bordeaux-Sud Ouest ( email )

351, cours de la Liberation
Bordeaux, 33405
France
+33 05 40 00 21 13 (Phone)

HOME PAGE: http://www.math.u-bordeaux1.fr/~delmoral/

University of Bordeaux - University of Bordeaux 1

351 cours de la Libération
33405 TALENCE cedex
France

Bruno Remillard (Contact Author)

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

Sylvain Rubenthaler

Université de Nice Sophia Antipolis ( email )

Nice
France

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
175
Abstract Views
1,402
rank
203,205
PlumX Metrics