Simulate Bates sample paths by Euler approximation
[
simulates Paths
,Times
,Z
,N
] = simByEuler(MDL
,NPeriods
)NTrials
sample paths of Bates bivariate models driven
by NBrowns
Brownian motion sources of risk and
NJumps
compound Poisson processes representing the arrivals
of important events over NPeriods
consecutive observation
periods. The simulation approximates continuous-time stochastic processes by the
Euler approach.
Bates models are bivariate composite models. Each Bates model consists of two coupled univariate models.
One model is a geometric Brownian motion (gbm
) model with a stochastic
volatility function and jumps.
This model usually corresponds to a price process whose volatility (variance rate) is governed by the second univariate model.
The other model is a Cox-Ingersoll-Ross (cir
) square root diffusion
model.
This model describes the evolution of the variance rate of the coupled Bates price process.
This simulation engine provides a discrete-time approximation of the underlying
generalized continuous-time process. The simulation is derived directly from the
stochastic differential equation of motion. Thus, the discrete-time process approaches
the true continuous-time process only as DeltaTimes
approaches
zero.
[1] Deelstra, Griselda, and Freddy Delbaen. “Convergence of Discretized Stochastic (Interest Rate) Processes with Stochastic Drift Term.” Applied Stochastic Models and Data Analysis. 14, no. 1, 1998, pp. 77–84.
[2] Higham, Desmond, and Xuerong Mao. “Convergence of Monte Carlo Simulations Involving the Mean-Reverting Square Root Process.” The Journal of Computational Finance 8, no. 3, (2005): 35–61.
[3] Lord, Roger, Remmert Koekkoek, and Dick Van Dijk. “A Comparison of Biased Simulation Schemes for Stochastic Volatility Models.” Quantitative Finance 10, no. 2 (February 2010): 177–94.