Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes
Coauthor(s): O. Kaya.
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. This paper suggests 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 our method. Specifically, our method
achieves an O(s^(-1/2)) convergence rate, where $s$ is the
total computational budget. The convergence rate for the Euler
discretization method is O(s^(-1/3)) or slower, depending
on the model coefficients and option payoff function.
Source: Operations Research
Broadie, Mark, and O. Kaya. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes." Operations Research 54, no. 2 (April 2006): 217-231.