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Keywords
(10)
Asian Option
Control Variates
Design and Implementation
High Dimensionality
Monte Carlo
Monte Carlo Simulation
Option Pricing
Path Dependence
Variance Reduction
Variance Reduction Techniques
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Pathdependent Option Price and Sensitivity Estimation through Structured Database MonteCarlo Simulation(SDMC)
Pathdependent Option Price and Sensitivity Estimation through Structured Database MonteCarlo Simulation(SDMC),Gang Zhao,Pirooz Vakili
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Pathdependent Option Price and Sensitivity Estimation through Structured Database MonteCarlo Simulation(SDMC)
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Gang Zhao
,
Pirooz Vakili
Monte Carlo simulation
has been widely used in nancial derivative and sensitivity(greek) evaluation, especially for pathdependent 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 payo 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 resampling 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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