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April 2021 Precise asymptotics: Robust stochastic volatility models
P. K. Friz, P. Gassiat, P. Pigato
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Ann. Appl. Probab. 31(2): 896-940 (April 2021). DOI: 10.1214/20-AAP1608

Abstract

We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of Bayer et al. (Math. Finance 30 (2020) 782–832) In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, Inahama–Kawabi on rough path space. When applied to rough volatility models, for example, in the setting of Bayer, Friz and Gatheral (Quant. Finance 16 (2016) 887–904) and Forde–Zhang (SIAM J. Financial Math. 8 (2017) 114–145), one obtains precise asymptotics for European options which refine known large deviation asymptotics.

Funding Statement

We gratefully acknowledge financial support of European Research Council Grant CoG-683164 (PKF and PP) and ANR-16-CE40-0020-01 (PG).

Acknowledgements

We are also grateful to the anonymous reviewer for his/her careful reading.

Citation

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P. K. Friz. P. Gassiat. P. Pigato. "Precise asymptotics: Robust stochastic volatility models." Ann. Appl. Probab. 31 (2) 896 - 940, April 2021. https://doi.org/10.1214/20-AAP1608

Information

Received: 1 October 2018; Revised: 1 April 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1608

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Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2021
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