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Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation

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  • Ling Zhi Liang
  • Damiaan Lemmens
  • Jacques Tempere

Abstract

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer option under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential.

Suggested Citation

  • Ling Zhi Liang & Damiaan Lemmens & Jacques Tempere, 2011. "Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation," Papers 1101.3713, arXiv.org.
    • Handle: RePEc:arx:papers:1101.3713
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    Cited by:

    1. Ma, Jingtang & Deng, Dongya & Lai, Yongzeng, 2015. "Explicit approximate analytic formulas for timer option pricing with stochastic interest rates," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 1-21.
    2. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    3. 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.
    4. 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.
    5. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    6. Li, Minqiang & Mercurio, Fabio, 2013. "Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models," MPRA Paper 47465, University Library of Munich, Germany.
    7. 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.
    8. 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.

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