Functional Convergence of Snell Envelopes: Applications to American Options Approximations

Finance and Stochastics, Vol. 2, No. 3 (1998)

Posted: 9 Jun 1998

See all articles by Sabrina Mulinacci

Sabrina Mulinacci

Università Cattolica del Sacro Cuore di Milano

Maurizio Pratelli

University of Pisa - Department of Mathematics

Abstract

The main result of the paper is a stability theorem for the Snell envelope under convergence in distribution of the underlying processes: more precisely, we prove that if a sequence $(X^n)$ of stochastic processes converges in distribution for the Skorokhod topology to a process $X$ and satisfies some additional hypotheses, the sequence of Snell envelopes converges in distribution for the Meyer-Zheng topology to the Snell envelope of $X$ (a brief account of this rather neglected topology is given in the appendix). When the Snell envelope of the limit process is continuous, the convergence is in fact in the Skorokhod sense. This result is illustrated by several examples of approximations of the American options prices; we give moreover a kind of robustness of the optimal hedging portfolio for the American put in the Black and Scholes model.

JEL Classification: G13

Suggested Citation

Mulinacci, Sabrina and Pratelli, Maurizio, Functional Convergence of Snell Envelopes: Applications to American Options Approximations. Finance and Stochastics, Vol. 2, No. 3 (1998), Available at SSRN: https://ssrn.com/abstract=88071

Sabrina Mulinacci (Contact Author)

Università Cattolica del Sacro Cuore di Milano ( email )

20123 Milano
Italy

Maurizio Pratelli

University of Pisa - Department of Mathematics

Via Buonarroti 2
I-56126 Pisa
Italy

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

Paper statistics

Abstract Views
755
PlumX Metrics