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The escape problem under stochastic volatility: the Heston model

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  • Jaume Masoliver
  • Josep Perello

Abstract

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.

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File URL: http://arxiv.org/pdf/0807.1014
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0807.1014.

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Date of creation: Jul 2008
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Publication status: Published in Phys. Rev. E 78, 056104 (2008)
Handle: RePEc:arx:papers:0807.1014

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Web page: http://arxiv.org/

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Cited by:
  1. Devreese, J.P.A. & Lemmens, D. & Tempere, J., 2010. "Path integral approach to Asian options in the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 389(4), pages 780-788.
  2. Kim, Min Jae & Kim, Sehyun & Jo, Yong Hwan & Kim, Soo Yong, 2011. "Dependence structure of the commodity and stock markets, and relevant multi-spread strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 390(21), pages 3842-3854.

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