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Pathwise moderate deviations for option pricing

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  • Antoine Jacquier
  • Konstantinos Spiliopoulos

Abstract

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling enables us to transfer these results into small‐time, large‐time, and tail asymptotics for diffusions, as well as for option prices and realized variances. In passing, we highlight some intuitive relationships between moderate deviations rate functions and their large deviations counterparts; these turn out to be useful for numerical purposes, as large deviations rate functions are often difficult to compute.

Suggested Citation

  • Antoine Jacquier & Konstantinos Spiliopoulos, 2020. "Pathwise moderate deviations for option pricing," Mathematical Finance, Wiley Blackwell, vol. 30(2), pages 426-463, April.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:2:p:426-463
    DOI: 10.1111/mafi.12228
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    Cited by:

    1. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    2. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.

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