Convergence of Numerical Methods for Valuing Path-Dependent Options Using Interpolation

Authors: Forsyth P.A.¹; Vetzal K.R.²; Zvan R.³

Source: Review of Derivatives Research, Volume 5, Number 3, 2002 , pp. 273-314(42)

Publisher: Springer

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Abstract:

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected inappropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature.

Keywords: Convergance; forward shooting grid; interpolation; option pricing; path-dependence

Language: English

Document Type: Research article

Affiliations: 1: Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1 E-mail: paforsyt@elora.math.uwaterloo.ca 2: Centre for Advanced Studies in Finance, University of Waterloo, Waterloo, ON, Canada N2L 3G1 E-mail: kvetzal@watarts.uwaterloo.ca 3: Financial Analytics and Structured Transactions, Bear Stearns, 383 Madison Avenue, New York, NY, USA 10179 E-mail: rzvan@bear.com

Publication date: 2002-01-01