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Closed-Form Approximation Of Perpetual Timer Option Prices

Author

Listed:
  • MINQIANG LI

    (Derivatives Research, Bloomberg LP. 731 Lexington Avenue, New York City, New York, 10022, USA)

  • FABIO MERCURIO

    (Derivatives Research, Bloomberg LP. 731 Lexington Avenue, New York City, New York, 10022, USA)

Abstract

We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand Black–Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate, especially when the volatility of variance is not large.

Suggested Citation

  • Minqiang Li & Fabio Mercurio, 2014. "Closed-Form Approximation Of Perpetual Timer Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500265
    DOI: 10.1142/S0219024914500265
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    References listed on IDEAS

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    1. Minqiang Li, 2015. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(6), pages 582-595, June.
    2. Minqiang Li & Fabio Mercurio, 2015. "Analytic Approximation of Finite‐Maturity Timer Option Prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(3), pages 245-273, March.
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    4. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
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    Cited by:

    1. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Pingping Zeng & Yue Kuen Kwok & Wendong Zheng, 2015. "Fast Hilbert Transform Algorithms For Pricing Discrete Timer Options Under Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-26, November.
    3. Wendong Zheng & Pingping Zeng, 2016. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 344-373, September.

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