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Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models

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  • Li, Minqiang
  • Mercurio, Fabio

Abstract

We develop an asymptotic expansion technique for pricing timer options under general stochastic volatility models around small volatility of variance. Closed-form approximation formulas have been obtained for the Heston model and the 3/2-model. 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.

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File URL: http://mpra.ub.uni-muenchen.de/47465/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47465.

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Date of creation: 2013
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Handle: RePEc:pra:mprapa:47465

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Keywords: Timer Option; Closed-Form Approximation; Perturbation;

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  1. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
  2. 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.
  3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  4. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
  5. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
  6. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
  7. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
  8. Avi Bick, 1995. "Quadratic-Variation-Based Dynamic Strategies," Management Science, INFORMS, vol. 41(4), pages 722-732, April.
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