Connecting discrete and continuous path-dependent options

Paul Glasserman, S.G. Kou () and Mark Broadie
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Paul Glasserman: Graduate School of Business, Columbia University, New York, NY 10027, USA
S.G. Kou: Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1027, USA
Mark Broadie: Graduate School of Business, Columbia University, New York, NY 10027, USA

Finance and Stochastics, 1999, vol. 3, issue 1, 55-82

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.

Keywords: Barrier options; lookback options; continuity corrections; trinomial trees (search for similar items in EconPapers)
JEL-codes: C63 G12 G13 (search for similar items in EconPapers)
Date: 1998-11-17
Note: received: December 1996; final version received: December 1997
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