PLENARY LECTURES Exact Simulation of Financial Models with Stochastic Volatility and other Affine Jump Diffusion Models

The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level. In this talk we present a method for the exact simulation of the stock price and variance under Heston’s stochastic volatility model and other affine jump diffusion processes. The sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security. We compare our method with the more conventional Euler discretization method and demonstrate the faster convergence rate of the error in this method. (This is joint work with Ozgur Kaya.)