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The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes

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  • Yusho Kagraoka

    (Faculty of Economics, Musashi University, Tokyo 176-8534, Japan)

Abstract

In option pricing models with correlated stochastic processes, an option premium is commonly a solution to a partial differential equation (PDE) with mixed derivatives in more than two space dimensions. Alternating direction implicit (ADI) finite difference methods are popular for solving a PDE with more than two space dimensions; however, it is not straightforward to employ the ADI method for solving a PDE with mixed derivatives. The aim of this study is to find out which numerical method would be appropriate to solve PDEs with mixed derivatives based on the accuracy of the solutions and the computation time. This study applies the fractional step method and the radial basis functions to solve a PDE with a mixed derivative, and investigates the efficiency of these numerical methods. Numerical experiments are conducted by applying these methods to exchange option pricing; exchange options are selected because the exchange option premium has an analytical form. The numerical results show that the both methods calculate premiums with high accuracy in the presence of mixed derivatives. The fractional step method calculates the option premium more accurately and much faster than the radial basis functions. Therefore, from the numerical experiments, this study concludes that the fractional step method is more appropriate than the radial basis functions for solving a PDE with a mixed derivative.

Suggested Citation

  • Yusho Kagraoka, 2020. "The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes," IJFS, MDPI, vol. 8(4), pages 1-13, December.
    • Handle: RePEc:gam:jijfss:v:8:y:2020:i:4:p:77-:d:454494
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    References listed on IDEAS

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    1. Raymond Brummelhuis & Ron T. L. Chan, 2014. "A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(3), pages 238-269, July.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    5. Ron Tat Lung Chan, 2016. "Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 47(4), pages 623-643, April.
    6. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    7. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.
    8. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    9. Ron Chan & Simon Hubbert, 2014. "Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme," Review of Derivatives Research, Springer, vol. 17(2), pages 161-189, July.
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