A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing

We consider the problem of estimating 𝔼[f(U1, …, Ud)], where (U1, …, Ud) 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, …, Ud) 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, …, Ud) 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.