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We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with non-zero correlation and sublinear growth for the volatility coefficient, using the Donsker-Varadhan[DV83] 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(OU) 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 Lévy process. ‡

Large-time option pricing using the Donsker–Varadhan LDP—correlated stochastic volatility with stochastic interest rates and jumps