Large deviation principle for stochastic differential equations driven by stochastic integrals

Abstract

In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP for many class of rough volatility models, and it characterizes the asymptotic behavior of implied volatility. First, we introduce a new concept called $\alpha$-Uniformly Exponentially Tightness, and prove the LDP for stochastic integrals on H\"{o}lder spaces. Second, we apply this type of LDP to deduce the LDP for stochastic differential equations driven by stochastic integrals in one dimension. Finally, we derive the asymptotic behavior of the implied volatility as an application of main results.