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Large deviations for some fast stochastic volatility models by viscosity methods

Authors :
Bardi, Martino
Cesaroni, Annalisa
Ghilli, Daria
Publication Year :
2014

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.

Subjects

Subjects :
Mathematics - Analysis of PDEs

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1405.3206
Document Type :
Working Paper