Exact Simulation of the Multifactor Ornstein–Uhlenbeck Driven Stochastic Volatility Model

The classic exact simulation scheme for the Ornstein--Uhlenbeck driven stochastic volatility model is designed for the single volatility factor case. Extension to the multifactor case results in a cumbersome procedure requiring multiple numerical inversions of Laplace transforms and subsequent random sampling through numerical methods, resulting in it being perceptively slow to run. Moreover, for each volatility factor, the error is controlled by two parameters, ensuring difficult control of the bias. In this paper, we propose a new exact simulation scheme for the multifactor Ornstein--Uhlenbeck driven stochastic volatility model that is easier to implement, faster to run, and allows for an improved control of the error, which, in contrast to the existing method, is controlled by only one parameter, regardless of the number of volatility factors. Numerical results show that the proposed approach is three times faster than the original approach when one volatility factor is considered and 11 times faster when four volatility factors are considered, while still being theoretically exact.