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

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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