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

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.