Small time asymptotics for an additive functional of a fast diffusion process: moderate, large and superlarge deviations
Monday, October 22, 2012 - 10:45am - 11:35am
Recent papers by Feng, Forde and Fouque (SIAM J Financial Math, 2010) and Feng, Fouque and Kumar (Ann. Appl. Prob, 2012) have obtained large deviation results for the small time asymptotic behavior for the log stock price in a fast mean-reverting stochastic volatility model. These results involve specific assumptions about the rate of growth of the speed parameter in the volatility process as the small time decreases to zero. It turns out that a simple time change argument converts the original problem into one concerning the large time asymptotic behavior of a related additive functional of the (rate 1) diffusion process. The scenarios described in the papers above correspond to large and moderate deviations of this additive functional away from its ergodic limit. We will discuss briefly some recent results for the case of superlarge deviations. This is joint work with Jerome Grand’Maison (University of Southern California).