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Valuation of power options under Heston's stochastic volatility model

Author

Listed:
  • Kim, Jerim
  • Kim, Bara
  • Moon, Kyoung-Sook
  • Wee, In-Suk

Abstract

We derive semi-analytic solutions for power option prices under the Heston model; specifically, the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment. Unlike the majority of stochastic volatility models, there remains a significant problem to check the existence of moments of assets prices of order higher than one. Fortunately, the moment explosion property under the Heston model is examined systematically in Andersen and Piterbarg (2000). Incorporating with their results, we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite. In case that the corresponding moment explodes, we provide two numerical methods to derive prices of power put and capped power call options. In spite of a simple idea, numerical examples show that the approximations are extremely accurate and efficient.

Suggested Citation

  • Kim, Jerim & Kim, Bara & Moon, Kyoung-Sook & Wee, In-Suk, 2012. "Valuation of power options under Heston's stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1796-1813.
  • Handle: RePEc:eee:dyncon:v:36:y:2012:i:11:p:1796-1813
    DOI: 10.1016/j.jedc.2012.05.005
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    References listed on IDEAS

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    1. Clark, Todd E. & Davig, Troy, 2011. "Decomposing the declining volatility of long-term inflation expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 981-999, July.
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    3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
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    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
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    Cited by:

    1. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    2. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    3. repec:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500244 is not listed on IDEAS
    4. repec:eee:apmaco:v:286:y:2016:i:c:p:257-264 is not listed on IDEAS

    More about this item

    Keywords

    Power option; Stochastic volatility; Heston model; Change of numeraire; Fourier transform;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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