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Path-dependent Option Price and Sensitivity Estimation through Structured Database Monte-Carlo Simulation(SDMC)

Path-dependent Option Price and Sensitivity Estimation through Structured Database Monte-Carlo Simulation(SDMC),Gang Zhao,Pirooz Vakili

Path-dependent Option Price and Sensitivity Estimation through Structured Database Monte-Carlo Simulation(SDMC)  
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Monte Carlo simulation has been widely used in nancial derivative and sensitivity(greek) evaluation, especially for path-dependent options. However, the convergence speed of standard MC method is only p n. The proposed methods involves a new approach to the design and implementation of variance reduction algorithms for high dimensional Monte Carlo simulation. We seek to obtain generic variance reducing algorithms that rely more on computational construction than discovery of specic features. We consider the (Asian) option pay-o as functions of a random input (variable, vector, path) and a model parameter (scalar or vector). Our approach, called Structured Database Monte Carlo (SDMC), involves generating a large database of random inputs, structuring the database using sample values at a nominal parameter value, and then using the structure to design eective variance reducing algorithms. Such algorithms are used for estimation at parameters in a neighborhood of the nominal and involve re-sampling from the database. We consider variance reduction techniques of stratication, stratication combined with control variate in this setting. Our results show that the direct application of our approach, or appropriate modications in instances involving discontinuity with respect to the parameter, result in signicant eciency gains. We have obtained some convergence results for the algorithms in a general setting and show that the SDMC approach may be extended to cases where perturbation is in model dynamics rather than model parameters.
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