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Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching

机译：隐马尔可夫体制转换的随机利率和波动率模型下的期权定价

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摘要

In this paper we discuss an option pricing problem in a hidden Markovian regime-switching model with a stochastic interest rate and volatility. Regime switches are attributed to structural changes in an hidden economic environment and are described by a continuous-time, finite-state, unobservable Markov chain. The model is then applied to the valuation of a standard European option. By means of the standard separation principle, filtering and option valuation problems are separated. Robust filters for the hidden states of the economy and their robust filtered estimates of unknown parameters from the expectation maximization algorithm are presented based on standard techniques in filtering theory. Then an explicit expression of a conditional characteristic function relevant to option pricing is presented and the valuation of the option is discussed using the inverse Fourier transformation approach. Using the limiting behavior of the conditional characteristic function, an efficient implementation of the transform inversion integral is considered. Numerical experiments are given to illustrate the flexibility of filtering algorithms and the significance of regime-switching in option pricing.
机译：在本文中，我们讨论了具有随机利率和波动性的隐马尔可夫政权转换模型中的期权定价问题。体制转换归因于一个隐藏的经济环境中的结构性变化，并由连续时间，有限状态，不可观察的马尔可夫链描述。然后将该模型应用于标准欧洲期权的估值。通过标准分离原理，可以将过滤和期权评估问题分离。基于滤波理论中的标准技术，提出了针对经济隐患的鲁棒滤波器及其对期望参数的未知参数的鲁棒滤波估计。然后给出了与期权定价有关的条件特征函数的显式表达式，并使用逆傅立叶变换方法讨论了期权的估值。使用条件特征函数的极限行为，可以考虑有效地实现变换反演积分。数值实验表明了滤波算法的灵活性以及期权定价中制度转换的重要性。

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  • 来源
    《Computational economics》 |2019年第2期|555-586|共32页
  • 作者

    Zhu Dong-Mei; Lu Jiejun; Ching Wai-Ki; Siu Tak-Kuen;

  • 作者单位

    Southeast Univ, Sch Management & Econ, Nanjing, Jiangsu, Peoples R China;

    Univ Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Pokfulam, Pokfulam Rd, Hong Kong, Peoples R China;

    Univ Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Pokfulam, Pokfulam Rd, Hong Kong, Peoples R China|Hughes Hall,Wollaston Rd, Cambridge, England|Beijing Univ Chem Technol, Sch Econ & Management, North Third Ring Rd, Beijing, Peoples R China;

    Macquarie Univ, Fac Business & Econ, Dept Appl Finance & Actuarial Studies, Sydney, NSW 2109, Australia;

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  • 正文语种 eng
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  • 关键词

    Option pricing; Hidden Markov model (HMM); Regime-switching; Characteristic function; Fourier transformation;

    机译：选项定价;隐藏的马尔可夫模型（嗯）;政权切换;特征函数;傅里叶变换;

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