Calculus of Variations and Geometric Measure Theory

M. Bardi - A. Cesaroni - D. Ghilli

Large deviations for some fast stochastic volatility models by viscosity methods

created by bardi on 14 May 2014
modified on 15 May 2015


Published Paper

Inserted: 14 may 2014
Last Updated: 15 may 2015

Journal: Discrete Contin. Dyn. Syst.
Volume: 35
Number: 9
Pages: 3965--3988
Year: 2015
Doi: 10.3934/dcds.2015.35.3965


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.