American Options with Stopping Time Constraints

19 Pages Posted: 12 Sep 2005

See all articles by Daniel Egloff

Daniel Egloff

QuantAlea GmbH

Markus Leippold

University of Zurich; Swiss Finance Institute

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich

Date Written: 2005

Abstract

This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi, Robin and Sun [21] we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We suggest a new Monte Carlo method to numerically calculate the option value also for multidimensional Markov processes. Because of presence of stopping time constraints the classical Longstaff-Schwartz least-square Monte Carlo algorithm or its extension introduced in [7] cannot be directly applied. We adapt the Longstaff-Schwartz algorithm to solve the stochastic Cauchy-Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process.

Keywords: American options, optimal stopping under constraints, out-performance options, management options

JEL Classification: C60; G13

Suggested Citation

Egloff, Daniel and Leippold, Markus and Farkas, Walter, American Options with Stopping Time Constraints (2005). Available at SSRN: https://ssrn.com/abstract=798124 or http://dx.doi.org/10.2139/ssrn.798124

Daniel Egloff (Contact Author)

QuantAlea GmbH ( email )

Wasserfuristrasse 42
Wiesendangen, 8542
Switzerland
+41 44 520 0117 (Phone)

Markus Leippold

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Walter Farkas

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

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