A Wiener measure theoretic approach to pricing extreme-value-related derivatives

Authors:
Nan Chen;Zhengyu Huang
Affiliations:
Chinese University of Hong Kong, Shatin, Hong Kong;Chinese University of Hong Kong, Shatin, Hong Kong
Venue:
Winter Simulation Conference
Year:
2009

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Abstract

Discretization schemes converge slowly when simulating extreme values for stochastic differential equations. Using a Wiener measure decomposition approach, this paper constructs an unbiased estimator for pricing extreme-value-related derivatives, such as barrier and lookback options, under a diffusion market model. A strong condition on the coefficients is needed in the derivation of the estimator. We also propose a truncation technique to remove this requirement and show that the truncation error decays exponentially. The numerical experiments reveal that this estimator is accurate and efficient.