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Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching

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  • Xuerong Mao
  • Aubrey Truman
  • Chenggui Yuan

Abstract

Stochastic differential equations (SDEs) under regime-switching have recently been developed to model various financial quantities. In general, SDEs under regime-switching have no explicit solutions, so numerical methods for approximations have become one of the powerful techniques in the valuation of financial quantities. In this paper, we will concentrate on the Euler-Maruyama (EM) scheme for the typical hybrid mean-reverting θ -process. To overcome the mathematical difficulties arising from the regime-switching as well as the non-Lipschitz coefficients, several new techniques have been developed in this paper which should prove to be very useful in the numerical analysis of stochastic systems.

Suggested Citation

  • Xuerong Mao & Aubrey Truman & Chenggui Yuan, 2006. "Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-20, July.
    • Handle: RePEc:hin:jnijsa:080967
    DOI: 10.1155/JAMSA/2006/80967
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    Cited by:

    1. Peyman Alipour & Ali Foroush Bastani, 2023. "Value-at-Risk-Based Portfolio Insurance: Performance Evaluation and Benchmarking Against CPPI in a Markov-Modulated Regime-Switching Market," Papers 2305.12539, arXiv.org.
    2. Liu Xiangdong & Mi Zeyu & Chen Huida, 2020. "A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions," Journal of Systems Science and Information, De Gruyter, vol. 8(1), pages 17-32, February.

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