First-passage and risk evaluation under stochastic volatility
AbstractWe solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the non-existence of a mean first-passage time. One significant result is the evidence of extreme deviations --which implies a high risk of default-- when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0902.2735.
Date of creation: Feb 2009
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Publication status: Published in Phys. Rev. E 80, 016108 (2009) [15 pages]
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-26 (All new papers)
- NEP-RMG-2009-09-26 (Risk Management)
- NEP-UPT-2009-09-26 (Utility Models & Prospect Theory)
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- 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, vol. 390(21), pages 3842-3854.
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