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September  2015, 35(9): 3965-3988. doi: 10.3934/dcds.2015.35.3965

## Large deviations for some fast stochastic volatility models by viscosity methods

 1 Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35133 Padova, Italy, Italy, Italy

Received  May 2014 Revised  September 2014 Published  April 2015

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 homogenization 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.
Citation: Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3965-3988. doi: 10.3934/dcds.2015.35.3965
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