A CENTRAL LIMIT THEOREM FOR LATIN HYPERCUBE SAMPLING WITH DEPENDENCE AND APPLICATION TO EXOTIC BASKET OPTION PRICING

Abstract

We consider the problem of estimating 𝔼[f(U¹, …, U^d)], where (U¹, …, U^d) denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of dependent components of the random vector (U¹, …, U^d) one can achieve more accurate results by using Latin hypercube sampling with dependence (LHSD). We state a central limit theorem for the d-dimensional LHSD estimator, by this means generalising a result of Packham and Schmidt. Furthermore we give conditions on the function f and the distribution of (U¹, …, U^d) under which a reduction of variance can be achieved. Finally we compare the effectiveness of Monte Carlo and LHSD estimators numerically in exotic basket option pricing problems.