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Optimal stopping time with stochastic volatility

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  • Zhang, Ran
  • Xu, Shuang

Abstract

This paper demonstrates how to convert a path-dependent optimal stopping time problem into a path-independent problem using a transformation analysis method. We test this method to deal with several problems, especially those in stochastic volatility environments. We introduce stochastic state variables into volatility dynamics and analyse the influence of state-variable volatile characters on investment stopping boundaries. For arbitrary coefficient circumstances, we set up a Riccati equation that satisfies the transformation. For circumstances involving Heston stochastic-volatility, we propose an analytical solution. This paper extends research on the optimal investment stopping issue to a stochastic investment opportunity environment. Our proposed method can enhance the ability of optimal investment stopping theory to describe the real capital market.

Suggested Citation

  • Zhang, Ran & Xu, Shuang, 2014. "Optimal stopping time with stochastic volatility," Economic Modelling, Elsevier, vol. 41(C), pages 319-328.
    • Handle: RePEc:eee:ecmode:v:41:y:2014:i:c:p:319-328
    DOI: 10.1016/j.econmod.2014.05.016
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    More about this item

    Keywords

    Investment stopping time; Optimal selling rule; Stochastic volatility;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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