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

L. Z. J. Liang1, D. Lemmens1, and J. Tempere1,2

  • 1TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
  • 2Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Phys. Rev. E 83, 056112 – Published 18 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.056112

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 options 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.

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      Phys. Rev. E 83, 056112– Published 18 May, 2011
      • Received 19 January 2011

      ©2011 American Physical Society

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