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A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions

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  • Kirkby, J. Lars
  • Nguyen, Dang H.
  • Nguyen, Duy

Abstract

Continuous time Markov Chain (CTMC) approximation techniques have received increasing attention in the option pricing literature, due to their ability to solve complex pricing problems, although existing approaches are mostly limited to one or two dimensions. This paper develops a general methodology for modeling and pricing financial derivatives which depend on systems of stochastic diffusion processes. This is accomplished with a general decorrelation procedure, which reduces the system of correlated diffusions to an uncorrelated system. This enables simple and efficient approximation of the driving processes by univariate CTMC approximations. Weak convergence of the approximation is demonstrated, with second order convergence in space. Numerical experiments demonstrate the accuracy and efficiency of the method for various European and early-exercise options in two and three dimensions.

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  • Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304318
    DOI: 10.1016/j.amc.2020.125472
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    8. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    9. Kirkby, J.L. & Nguyen, Dang H. & Nguyen, Duy & Nguyen, Nhu N., 2022. "Maximum likelihood estimation of diffusions by continuous time Markov chain," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    10. Christian Meier & Lingfei Li & Gongqiu Zhang, 2021. "Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximation," Papers 2107.04260, arXiv.org.

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