simByEuler
Simulate Bates
sample paths by Euler
approximation
Description
[
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.
[
specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.Paths
,Times
,Z
,N
] = simByEuler(___,Name,Value
)
You can perform quasi-Monte Carlo simulations using the name-value arguments for
MonteCarloMethod
, QuasiSequence
, and
BrownianMotionMethod
. For more information, see Quasi-Monte Carlo Simulation.
Examples
Input Arguments
Name-Value Arguments
Output Arguments
More About
Algorithms
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 DeltaTime
approaches
zero.
References
[1] Deelstra, Griselda, and Freddy Delbaen. “Convergence of Discretized Stochastic (Interest Rate) Processes with Stochastic Drift Term.” Applied Stochastic Models and Data Analysis, Vol. 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, Vol. 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, Vol. 10, No. 2 (February 2010): 177–94.
Version History
Introduced in R2020aSee Also
Topics
- Implementing Multidimensional Equity Market Models, Implementation 5: Using the simByEuler Method
- Simulating Equity Prices
- Simulating Interest Rates
- Stratified Sampling
- Price American Basket Options Using Standard Monte Carlo and Quasi-Monte Carlo Simulation
- Base SDE Models
- Drift and Diffusion Models
- Linear Drift Models
- Parametric Models
- SDEs
- SDE Models
- SDE Class Hierarchy
- Quasi-Monte Carlo Simulation
- Performance Considerations