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Large deviations for some fast stochastic volatility models by viscosity methods

Abstract : We consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. We study the asymptotics of a logarithmic functional of the process by methods of the theory of homogenisation and singular perturbations for fully nonlinear PDEs. We point out three regimes depending on how fast the volatility oscillates relative to the horizon length. We prove a large deviation principle for each regime and apply it to the asymptotics of option prices near maturity.
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https://hal.inria.fr/hal-01122241
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, March 3, 2015 - 2:47:44 PM
Last modification on : Thursday, June 14, 2018 - 10:54:02 AM
Long-term archiving on: : Thursday, June 4, 2015 - 11:20:56 AM

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  • HAL Id : hal-01122241, version 1
  • ARXIV : 1405.3206

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Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. 2015. ⟨hal-01122241⟩

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