Liang L Z J, Lemmens D, Tempere J
TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056112. doi: 10.1103/PhysRevE.83.056112. Epub 2011 May 18.
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.
