LARGE-TIME OPTION PRICING USING THE DONSKER-VARADHAN LDP-CORRELATED STOCHASTIC VOLATILITY WITH STOCHASTIC INTEREST RATES AND JUMPS

We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with nonzero correlation and sublinear growth for the volatility coefficient, using the Donsker-Varadhan [Comm. Pure Appl. Math. 36 (1983) 183-212] LDP for the occupation measure of a Feller process under mild ergodicity conditions. We verify that these conditions are satisfied when the process driving the volatility is an Ornstein Uhlenbeck (013) process with a perturbed (sublinear) drift. We then translate these results into large-time asymptotics for call options and implied volatility and we verify our results numerically using Monte Carlo simulation. Finally, we extend our analysis to include a CIR short rate process and an independent driving Levy process.