Large deviations for fractional volatility models with non-Gaussian volatility driver

Multivariate Stochastic Volatility Models and Large Deviation Principles

“…It is organized as follows. In Subsections 10.1 and 10.2, we overview one-factor Gaussian models studied in [37] and one-factor non-Gaussian fractional models introduced in [35]. These subsections are auxiliary.…”

“…The model for the volatility process described in (10.3) is more general than the models considered in [35] and [37]. Unlike the latter models, the model in (10.3) is multidimensional, the restrictions on V and U are weaker than those in [35], and the volatility process in (10.3) is a mixture of volatility processes in the above-mentioned models.…”

“…In Subsections 10.1 and 10.2, we give a brief overview of onefactor Gaussian models and one-factor non-Gaussian fractional models, respectively. For more information about such models see [35,37,39]. In Subsection 10.3, we merge multivariate Gaussian models and multivariate non-Gaussian fractional models, and show that Theorem 4.1 holds for such mixtures.…”

“…0 ) is such that s i > 0 for all 1 ≤ i ≤ m. The meanings of the symbols appearing in the previous equation will be explained in Section 2. Stochastic volatility models are widely used in financial mathematics (see, e.g., [6,29,30,41,42,47,51,52]), and there is a rich literature devoted to applications of large deviation principles to the study of the asymptotic behavior of various quantities arising in finance (see, e.g., [2,18,28,33,35,37,38,39,40,43,44,59,62]). A stochastic model in (1.1) is characterized by the drift map b, the volatility map σ, and the volatility process Department of Mathematics, Ohio University, Athens OH 45701; e-mail: gulisash@ohio.edu 1 B.…”

“…It is clear that x 0 = (log s (1) 0 , • • • , s (m) 0 ). Various sample path LDPs are known for log-processes (see, e.g., [14,15,28,32,35,37,38,39,40,44]). Our main goal in the present paper is to obtain a universal sample path LDP for log-processes in multivariate stochastic volatility models that unifies the results established in the above-mentioned publications and also provides new results.…”