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IJSTR >> Volume 9 - Issue 3, March 2020 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

A Kernel Density Estimation-Based Approach To Option Pricing

[Full Text]



Soufiane Ouamaliche, Awatef Sayah



Asian Option, Feynman-Kac theorem, Kernel Density Estimation, Monte Carlo Simulations, Option Pricing, Roger & Shi PDE, Variance Reduction.



When used in option pricing, a classical Monte Carlo method fails to deliver highly accurate results even when variance reduction techniques are introduced. This lack of accuracy is particularly striking when one is dealing with exotic options. In this paper we aim at improving the quality of the price estimates given by Monte Carlo simulations within the regular Black & Scholes framework, through the use of an approach in which suitable weights are applied to adjust the numerical evaluation of the expected value stated by the Feynman-Kac theorem. Computing the said weights requires the use of an empirical density estimation, namely we will be using a kernel density estimator coupled with various kernels some of which are based on known probability density functions and others based on orthogonal polynomials. The suggested technique was applied to pricing an arithmetic Asian option and the achieved results were compared to prices computed via a classical Monte Carlo procedure, the target price being a well-known numerical solution of the Roger & Shi PDE. Our method has proved its success in providing more accurate prices for all of the test cases which implies that the use of the technique would probably be adequate for a wide variety of high-dimensional pricing problems.



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