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First-passage and risk evaluation under stochastic volatility

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  • Jaume Masoliver
  • Josep Perello

Abstract

We 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.

Suggested Citation

  • Jaume Masoliver & Josep Perello, 2009. "First-passage and risk evaluation under stochastic volatility," Papers 0902.2735, arXiv.org.
    • Handle: RePEc:arx:papers:0902.2735
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    Cited by:

    1. Zhong, Guang-Yan & He, Feng & Li, Jiang-Cheng & Mei, Dong-Cheng & Tang, Nian-Sheng, 2019. "Coherence resonance-like and efficiency of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Andrea Di Iura & Giulia Terenzi, 2022. "A Bayesian analysis of gain-loss asymmetry," SN Business & Economics, Springer, vol. 2(5), pages 1-23, May.
    3. Wu, Anshun & Dong, Yang & Luo, Yuhui & Zeng, Chunhua, 2020. "Fluctuations-induced regime shifts in the Endogenous Credit system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Andrea Giuseppe Di Iura & Giulia Terenzi, 2021. "A Bayesian analysis of gain-loss asymmetry," Papers 2104.06044, arXiv.org.
    5. 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.
    6. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Zhong, Guang-Yan & Li, Jiang-Cheng & Jiang, George J. & Li, Hai-Feng & Tao, Hui-Ming, 2018. "The time delay restraining the herd behavior with Bayesian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 335-346.
    8. Ko, Bonggyun & Song, Jae Wook, 2018. "A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 398-412.

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