create new SVJJ process

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Finance[SVJJProcess] - create new SVJJ process

	Calling Sequence
	SVJJProcess(, , r, theta, kappa, sigma, rho, lambda, alpha, beta, delta, t)

Parameters

	-	real constant; initial value of the return process
	-	non-negative constant; initial value of the variance
r	-	real constant; risk-neutral drift
theta	-	non-negative constant, algebraic expression or procedure; long-run mean of the volatility
kappa	-	positive constant; speed of mean reversion
sigma	-	real constant; volatility of the variance process
rho	-	non-negative constant; instantaneous correlation between the return process and the variance process
lambda	-	non-negative constant; jump intensity
alpha	-	non-negative constant; mean relative jump size
beta	-	real constant; standard deviation of the relative jump size
delta	-	real constant; jump size of the variance process
t	-	name; time variable

Description

•	The SVJJProcess command creates a new stochastic volatility process with jumps (SVJJ). This is a process governed by the stochastic differential equation (SDE)

where

–	is the risk-neutral drift,

–	is the long-run mean of the variance process,

–	is the speed of mean reversion of the variance process,

–	is the volatility of the variance process,

–	is the volatility jump size,

and

–	is the two-dimensional Wiener process with instantaneous correlation ,

–	is a Poisson process, independent of , with constant intensity ,

–	is a lognormal random variable with mean and variance .

•	The parameters , , and are related by the following equation

ln(1+mu) = alpha+(1/2)*beta^2

•	This process was introduced by A. Matytsin. Special cases of this process include

	Bates SVJ process
	Heston SV process

Compatibility

•	The Finance[SVJJProcess] command was introduced in Maple 15.

•	For more information on Maple 15 changes, see Updates in Maple 15.

Examples

First construct an SVJJ process with variable parameters. You will assign numeric values to these parameters later.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Generate 10 replications of the sample path and plot sample paths for the state variable and the variance process.

A := RTABLE(18446790986282556222, float[8], Array, rectangular, C_order, [], 3, 1 .. 10, 1 .. 2, 1 .. 31)

(13)

(14)

Consider different parameters.

(15)

(16)

(17)

(18)

Generate 10 replications of the sample path of the new process and plot sample paths for the state variable and the variance process.

A := RTABLE(18446790986282553206, float[8], Array, rectangular, C_order, [], 3, 1 .. 10, 1 .. 2, 1 .. 31)

(19)

	See Also
	Finance[BlackScholesProcess], Finance[BrownianMotion], Finance[Diffusion], Finance[Drift], Finance[ExpectedValue], Finance[GeometricBrownianMotion], Finance[HestonProcess], Finance[ItoProcess], Finance[SamplePath], Finance[SampleValues], Finance[SquareRootDiffusion], Finance[StochasticProcesses], Finance[WienerProcess]

References

Bates, D., Jumps and stochastic volatility: the exchange rate processes implicit in Deutschemark options, Review of Financial Studies, Volume 9, 69-107, 1996.

Duffie, D., Pan, J., and Singleton, K.J. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, Volume 68, 1343-1376, 2000.

Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.

Matytsin, A. Modelling volatility and volatility derivatives, Columbia Practitioners Conference on the Mathematics of Finance, 1999.

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