  In this article we consider the problem of pricing and hedging
high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We
assume a Black-Scholes market with time-dependent volatilities and show how to
compute the deltas by the aid of the Malliavin Calculus, extending the
procedure employed by Montero and Kohatsu-Higa (2003). Efficient
path-generation algorithms, such as Linear Transformation and Principal
Component Analysis, exhibit a high computational cost in a market with
time-dependent volatilities. We present a new and fast Cholesky algorithm for
block matrices that makes the Linear Transformation even more convenient.
Moreover, we propose a new-path generation technique based on a Kronecker
Product Approximation. This construction returns the same accuracy of the
Linear Transformation used for the computation of the deltas and the prices in
the case of correlated asset returns while requiring a lower computational
time. All these techniques can be easily employed for stochastic volatility
models based on the mixture of multi-dimensional dynamics introduced by Brigo
et al. (2004).
