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Efficient Semi-Discretization Techniques for Pricing European and American Basket Options

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  • Fazlollah Soleymani

    (Institute for Advanced Studies in Basic Sciences)

Abstract

This paper studies the valuation of option pricing problem in the presence of several assets. European- and American-style options are dealt with using high order semi-discretization techniques. We integrate the resulting system of semi-discretized ODEs in time with several time-stepping schemes such as explicit Euler method, explicit Runge–Kutta method, and the Runge–Kutta method with adaptive variable step sizes. Numerical results demonstrate that employing higher order semi-discretizations improves the computational performance of the multi-asset option pricing problems.

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  • Fazlollah Soleymani, 2019. "Efficient Semi-Discretization Techniques for Pricing European and American Basket Options," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1487-1508, April.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9819-4
    DOI: 10.1007/s10614-018-9819-4
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    References listed on IDEAS

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    1. Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "A Second-Order Difference Scheme for the Penalized Black–Scholes Equation Governing American Put Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 49-62, June.
    2. Darae Jeong & Minhyun Yoo & Junseok Kim, 2018. "Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 961-972, April.
    3. Xianming Sun & Siqing Gan, 2014. "An Efficient Semi-Analytical Simulation for the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 433-445, April.
    4. Rafael Company & Vera Egorova & Lucas J'odar & Fazlollah Soleymani, 2017. "Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach," Papers 1701.08545, arXiv.org.
    5. Kamille Sofie Tågholt Gad & Jesper Lund Pedersen, 2015. "Rationality Parameter for Exercising American Put," Risks, MDPI, vol. 3(2), pages 1-9, May.
    6. Rambeerich, N. & Tangman, D.Y. & Lollchund, M.R. & Bhuruth, M., 2013. "High-order computational methods for option valuation under multifactor models," European Journal of Operational Research, Elsevier, vol. 224(1), pages 219-226.
    7. Egorova, Yana, 2017. "Инвестирование Денежных Средств В Условиях Экономического Кризиса В 2017 Году," MPRA Paper 77648, University Library of Munich, Germany.
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