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We consider the problem of pricing path-dependent options on a basket ofunderlying assets using simulations. As an example we develop our studies usingAsian options. Asian options are derivative contracts in which the underlyingvariable is the average price of given assets sampled over a period of time.Due to this structure, Asian options display a lower volatility and aretherefore cheaper than their standard European counterparts. This paper is asurvey of some recent enhancements to improve efficiency when pricing Asianoptions by Monte Carlo simulation in the Black-Scholes model. We analyze thedynamics with constant and time-dependent volatilities of the underlying assetreturns. We present a comparison between the precision of the standard MonteCarlo method (MC) and the stratified Latin Hypercube Sampling (LHS). Inparticular, we discuss the use of low-discrepancy sequences, also known asQuasi-Monte Carlo method (QMC), and a randomized version of these sequences,known as Randomized Quasi Monte Carlo (RQMC). The latter has proven to be auseful variance reduction technique for both problems of up to 20 dimensionsand for very high dimensions. Moreover, we present and test a new pathgeneration approach based on a Kronecker product approximation (KPA) in thecase of time-dependent volatilities. KPA proves to be a fast generationtechnique and reduces the computational cost of the simulation procedure.

Monte Carlo Methods and Path-Generation techniques for Pricing Multi-asset Path-dependent Options