Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation
AbstractIn 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1101.3713.
Date of creation: Jan 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-30 (All new papers)
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- 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.
- Li, Minqiang, 2014. "Analytic Approximation of Finite-Maturity Timer Option Prices," MPRA Paper 54597, University Library of Munich, Germany.
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