Connecting Discrete and Continuous Path-Dependent Options

Posted: 25 Nov 1998

See all articles by Mark Broadie

Mark Broadie

Columbia University - Columbia Business School - Decision Risk and Operations

Paul Glasserman

Columbia Business School

Steven Kou

Boston University

Abstract

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete- and continuous-time prices which dramatically improve convergence to the accurate price.

JEL Classification: G13, C63, G12

Suggested Citation

Broadie, Mark and Glasserman, Paul and Kou, Steven, Connecting Discrete and Continuous Path-Dependent Options. Available at SSRN: https://ssrn.com/abstract=140262

Mark Broadie (Contact Author)

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States
212-854-4103 (Phone)

Paul Glasserman

Columbia Business School ( email )

3022 Broadway
403 Uris Hall
New York, NY 10027
United States
212-854-4102 (Phone)
212-316-9180 (Fax)

Steven Kou

Boston University ( email )

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Boston, MA 02215
United States
6173583318 (Phone)

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