Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model

This paper proposes a novel exact simulation method for the Ornstein–Uhlenbeck driven stochastic volatility model. To accomplish this goal, our task hinges on properly handling the Ornstein–Uhlenbeck volatility process. The major challenge involves conditionally sampling the integral of its square with respect to time given its marginal state as well as its integral with respect to time. We thus derive a closed-form Laplace transform of this conditional distribution via the techniques of changing probability measure as well as analytical extension. Then, we obtain the corresponding conditional cumulative distribution function via Fourier transform inversion and finally sample the distribution via the inverse transform method. We show that our method achieves a faster convergence rate of root-mean-square errors comparing with Euler discretization method, and apply it in the valuation of discretely monitored path-dependent options.