Large-time option pricing using the Donsker-Varadhan LDP-correlated stochastic volatility with stochastic interest rates and jumps. (English) Zbl 1357.91047

Summary: 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 LDP [M. D. Donsker and S. R. S. Varadhan, Commun. Pure Appl. Math. 36, 183–212 (1983; Zbl 0512.60068)] 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.


91G20 Derivative securities (option pricing, hedging, etc.)
60F10 Large deviations
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J60 Diffusion processes
60J25 Continuous-time Markov processes on general state spaces
60G51 Processes with independent increments; Lévy processes
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods


Zbl 0512.60068
Full Text: DOI Euclid