Asymptotics for multifactor Volterra type stochastic volatility models

Abstract

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti (J. Theor. Probab. 34(2):682–727). We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles.

Keywords:

• Large deviations
• Volterra type Gaussian processes
• multifactor stochastic volatility models

2010/2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 60F10
• 60G15
• 60G22

Acknowledgements

The authors thank Paolo Pigato for some hints and comments about the financial aspect of the problem.

Disclosure statement

No potential conflict of interest was reported by the authors.