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High-order computational methods for option valuation under multifactor models

Author

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  • Rambeerich, N.
  • Tangman, D.Y.
  • Lollchund, M.R.
  • Bhuruth, M.

Abstract

Many of the different numerical techniques in the partial differential equations framework for solving option pricing problems have employed only standard second-order discretization schemes. A higher-order discretization has the advantage of producing low size matrix systems for computing sufficiently accurate option prices and this paper proposes new computational schemes yielding high-order convergence rates for the solution of multi-factor option problems. These new schemes employ Galerkin finite element discretizations with quadratic basis functions for the approximation of the spatial derivatives in the pricing equations for stochastic volatility and two-asset option problems and time integration of the resulting semi-discrete systems requires the computation of a single matrix exponential. The computations indicate that this combination of high-order finite elements and exponential time integration leads to efficient algorithms for multi-factor problems. Highly accurate European prices are obtained with relatively coarse meshes and high-order convergence rates are also observed for options with the American early exercise feature. Various numerical examples are provided for illustrating the accuracy of the option prices for Heston’s and Bates stochastic volatility models and for two-asset problems under Merton’s jump-diffusion model.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:219-226
    DOI: 10.1016/j.ejor.2012.07.023
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    References listed on IDEAS

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    2. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    3. Kim, Junseok & Kim, Taekkeun & Jo, Jaehyun & Choi, Yongho & Lee, Seunggyu & Hwang, Hyeongseok & Yoo, Minhyun & Jeong, Darae, 2016. "A practical finite difference method for the three-dimensional Black–Scholes equation," European Journal of Operational Research, Elsevier, vol. 252(1), pages 183-190.
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    5. Company, Rafael & Egorova, Vera N. & Jódar, Lucas, 2021. "A front-fixing ETD numerical method for solving jump–diffusion American option pricing problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 69-84.
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    7. 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.
    8. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
    9. Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.
    10. 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.

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