Large deviation principle for Volterra type fractional stochastic volatility models

Archil Gulisashvili

Papers from arXiv.org

Abstract: We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $\sigma$ is globally H\"{o}lder-continuous and the process $\widehat{B}$ is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on $\sigma$ and $\widehat{B}$. We assume that $\sigma$ satisfies a mild local regularity condition, while the process $\widehat{B}$ is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process $\widehat{B}$, we derive a large deviation principle in the small-time regime. As an application, we obtain asymptotic formulas for binary options, call and put pricing functions, and the implied volatility in certain mixed regimes.

Date: 2017-10, Revised 2018-08
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (21)

Downloads: (external link)
http://arxiv.org/pdf/1710.10711 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1710.10711

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().