Quasi-Monte Carlo (QMC) method is playing an increasing role in the problemsof pricing and hedging of complex financial derivatives. These problems areusually of high dimensionality and discontinuities. The two factors maysignificantly deteriorate the performance of the QMC method. This paperdevelops a method that overcomes the challenges of the high dimensionality anddiscontinuities concurrently. For this purpose, a smoothing method is proposedto remove the discontinuities for some typical functions arising from financialengineering. To make the smoothing method applicable for more generalfunctions, a new path generation method is designed for simulating the paths ofthe underlying assets such that the resulting function has the required form.The new path generation method has an additional power to reduce the effectivedimension of the target function. Our proposed method caters for a largevariety of model specifications, including the Black-Scholes, exponentialnormal inverse Gaussian L'evy, and Heston models. Numerical experimentsdealing with these models show that in the QMC setting the proposed smoothingmethod in combination with the new path generation method can lead to adramatic variance reduction for pricing exotic options with discontinuouspayoffs and for calculating options' Greeks. The investigation on the effectivedimension and the related characteristics explains the significant enhancementof the combined procedure.
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