Before revision:  We establish a small-noise large deviation principle for the log-price, and under \widehat{B}  an additional assumption of the self-similarity of the process \widehat{B}, derive a similar large deviation principle in the small-time regime.
After revision:  We establish a small-noise large deviation principle for the log-price, and under . We assume that \sigma satisfies rather mild local regularity and growth conditions, while the process\widehat{B} an additional assumption of the self-similarity of the process \widehat{B}, derive a similar large deviation principle in the small-time regime.