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First-Order Asymptotics of Path-Dependent Derivatives in Multiscale Stochastic Volatility Environment

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  • Yuri F. Saporito

Abstract

In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent derivatives as well. Under general conditions, the first-order condition is represented by a conditional expectation that could be numerically evaluated. Moreover, if the path-dependence is not too severe, we are able to find path-dependent closed-form solutions equivalent to the fist-order approximation of path-independent options derived in Fouque et al. Additionally, we exemplify the results with Asian options and options on quadratic variation.

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  • Yuri F. Saporito, 2017. "First-Order Asymptotics of Path-Dependent Derivatives in Multiscale Stochastic Volatility Environment," Papers 1712.07320, arXiv.org.
    • Handle: RePEc:arx:papers:1712.07320
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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.
    2. Samy Jazaerli & Yuri F. Saporito, 2013. "Functional Ito Calculus, Path-dependence and the Computation of Greeks," Papers 1311.3881, arXiv.org, revised Jun 2018.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Yuri F. Saporito, 2020. "Pricing Path-Dependent Derivatives under Multiscale Stochastic Volatility Models: a Malliavin Representation," Papers 2005.04297, arXiv.org.
    2. Ofelia Bonesini & Antoine Jacquier & Chloe Lacombe, 2020. "A theoretical analysis of Guyon's toy volatility model," Papers 2001.05248, arXiv.org, revised Nov 2022.

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