Beh, Woan Lin and Pooi, Ah Hin * and Goh, K. L. (2014) Pricing of American call options using regression and numerical integration. Australian Journal of Basic & Applied Sciences, 8 (24). pp. 817. ISSN 19918178

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Abstract
Consider the American basket call option in the case where there are N underlying assets, the number of possible exercise times prior to maturity is finite, and the vector of N asset prices is modeled using a Levy process. A numerical method based on regression and numerical integration is proposed to estimate the price of the American option. In the proposed method, we first express the asset prices as nonlinear functions of N uncorrelated standard normal random variables. For a given set of timet asset prices, we next determine the timet continuation value by performing a numerical integration along the radial direction in the Ndimensional polar coordinate system for the N uncorrelated standard normal random variables, expressing the integrated value via a regression procedure as a function of the polar angles, and performing a numerical integration over the polar angles. The larger value of the continuation value and the timet immediate exercise value will then be the option value. The timet option values over the Ndimensional space may be represented by a quadratic function of the radial distance, with the coefficients of the quadratic function given by second degree polynomials in N1 polar angles. Partitioning the maturity time T into k* intervals of length Δt, we obtain the time(k1)Δt option value from the timekΔt option values for k= k*, k*1,…, 1. The time0 option value is then the price of the American option. It is found that the numerical results for the American option prices based on regression and numerical integration agree well with the simulation results, and exhibit a variation of the prices as we vary the nonnormality of the underlying distributions of the assets. To assess the accuracy of the computed price we may use estimated standard error of the computed American option price. The standard error will help us gauge whether the number of selected points along the radial direction and the number of selected polar angles are large enough to achieve the required level of accuracy for the computed American option price.
Item Type:  Article 

Additional Information:  First author is with Universiti Tunku Abdul Rahman; 2nd author is with Sunway University Business School; 3rd author is with the Dept. Applied Statistics, Faculty of Economics and Administration, Universiti Malaya. 
Uncontrolled Keywords:  American option pricing; simulation; numerical integration; Levy process; regression; Ndimensional polar coordinate system 
Subjects:  Q Science > QA Mathematics 
Divisions:  Sunway University > Sunway University Business School > Dept. Financial Mathematics & Statistics 
Depositing User:  Ms. Molly Chuah 
Date Deposited:  28 Mar 2016 05:33 
Last Modified:  28 Mar 2016 05:33 
URI:  http://eprints.sunway.edu.my/id/eprint/310 
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