Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method
American Journal of Applied Mathematics
Volume 4, Issue 4, August 2016, Pages: 181-185
Received: May 6, 2016; Accepted: May 20, 2016; Published: Jul. 13, 2016
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Michael Chimezie Anyanwu, Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
Roseline Ngozi Okereke, Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
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The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price and the stochastic interest rate, we obtain a pricing of pure discount bond available in the market. Our method of valuation is to apply eigenfunction expansion to the variable that describes the evolution of the interest rate, and Fourier transform to the variable that describes the log asset price.
Fourier Transform, Eigenfunction Expansion, Stochastic Interest Rate, Levy Process, Simple Harmonic Oscillator
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Michael Chimezie Anyanwu, Roseline Ngozi Okereke, Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method, American Journal of Applied Mathematics. Vol. 4, No. 4, 2016, pp. 181-185. doi: 10.11648/j.ajam.20160404.13
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