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A theoretical analysis of Guyon's toy volatility model

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  • Ofelia Bonesini
  • Antoine Jacquier
  • Chloe Lacombe

Abstract

We provide a thorough analysis of the path-dependent volatility model introduced by Guyon \cite{G17}, proving existence and uniqueness of a strong solution, characterising its behaviour at boundary points, providing asymptotic closed-form option prices as well as deriving small-time behaviour estimates.

Suggested Citation

  • Ofelia Bonesini & Antoine Jacquier & Chloe Lacombe, 2020. "A theoretical analysis of Guyon's toy volatility model," Papers 2001.05248, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2001.05248
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, October.
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    5. Yuri F. Saporito, 2018. "First-Order Asymptotics Of Path-Dependent Derivatives In Multiscale Stochastic Volatility Environment," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.
    6. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    7. Mohammed, Salah & Zhang, Tusheng, 2009. "Anticipating stochastic differential systems with memory," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2773-2802, September.
    8. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
    9. Yuri F. Saporito, 2017. "First-Order Asymptotics of Path-Dependent Derivatives in Multiscale Stochastic Volatility Environment," Papers 1712.07320, arXiv.org.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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