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Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models

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  • Giacomo Giorgio
  • Barbara Pacchiarotti
  • Paolo Pigato

Abstract

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra process. For this reason, we are able to apply such an LDP to two notable examples of non-self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion (Bayer, C., F. Harang, and P. Pigato. 2021. “Log-Modulated Rough Stochastic Volatility Models.” SIAM Journal on Financial Mathematics 12 (3): 1257–1284), and models where it is given as a function of a fractional Ornstein–Uhlenbeck (fOU) process (Gatheral, J., T. Jaisson, and M. Rosenbaum. 2018. “Volatility is Rough.” Quantitative Finance 18 (6): 933–949). In both cases, we derive consequences for short-maturity European option prices implied volatility surfaces and implied volatility skew. In the fOU case, we also discuss moderate deviations pricing and simulation results.

Suggested Citation

  • Giacomo Giorgio & Barbara Pacchiarotti & Paolo Pigato, 2023. "Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 123-152, May.
    • Handle: RePEc:taf:apmtfi:v:30:y:2023:i:3:p:123-152
    DOI: 10.1080/1350486X.2023.2299467
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    Cited by:

    1. Dugo, Ranieri & Giorgio, Giacomo & Pigato, Paolo, 2026. "The multivariate fractional Ornstein–Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    2. Ranieri Dugo & Giacomo Giorgio & Paolo Pigato, 2024. "The Multivariate Fractional Ornstein-Uhlenbeck Process," CEIS Research Paper 581, Tor Vergata University, CEIS, revised 28 Aug 2024.
    3. Martin Friesen & Stefan Gerhold & Kristof Wiedermann, 2024. "Small-time central limit theorems for stochastic Volterra integral equations and their Markovian lifts," Papers 2412.15971, arXiv.org.

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