simulate
Simulate multivariate stochastic differential equations (SDEs) for
SDE
, BM
, GBM
,
CEV
, CIR
, HWV
,
Heston
, SDEDDO
, SDELD
,
SDEMRD
, Merton
, or Bates
models
Description
[
simulates Paths
,Times
,Z
] = simulate(MDL
)NTrials
sample paths of NVars
correlated state variables, driven by NBrowns
Brownian motion
sources of risk over NPeriods
consecutive observation periods,
approximating continuous-time stochastic processes.
simulate
accepts any variable-length list of input arguments
that the simulation method or function referenced by the
SDE.Simulation
parameter requires or accepts. It passes this
input list directly to the appropriate SDE simulation method or user-defined
simulation function.
Examples
Input Arguments
Output Arguments
More About
Algorithms
This function simulates any vector-valued SDE of the form:
(1) |
X is an NVars-by-
1
state vector of process variables (for example, short rates or equity prices) to simulate.W is an NBrowns-by-
1
Brownian motion vector.F is an NVars-by-
1
vector-valued drift-rate function.G is an NVars-by-NBrowns matrix-valued diffusion-rate function.
References
[1] Ait-Sahalia, Y. “Testing Continuous-Time Models of the Spot Interest Rate.” The Review of Financial Studies, Spring 1996, Vol. 9, No. 2, pp. 385–426.
[2] Ait-Sahalia, Y. “Transition Densities for Interest Rate and Other Nonlinear Diffusions.” The Journal of Finance, Vol. 54, No. 4, August 1999.
[3] Glasserman, P. Monte Carlo Methods in Financial Engineering. New York, Springer-Verlag, 2004.
[4] Hull, J. C. Options, Futures, and Other Derivatives, 5th ed. Englewood Cliffs, NJ: Prentice Hall, 2002.
[5] Johnson, N. L., S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Vol. 2, 2nd ed. New York, John Wiley & Sons, 1995.
[6] Shreve, S. E. Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer-Verlag, 2004.
Version History
See Also
simByEuler
| simBySolution
| simBySolution
| sde
| merton
| bates
| bm
| gbm
| sdeddo
| sdeld
| cev
| cir
| heston
| hwv
| sdemrd