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Simulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme

`[`

simulates `Paths`

,`Times`

,`Z`

] = simByQuadExp(`MDL`

,`NPeriods`

)`NTrials`

sample paths of a Heston model driven by
two Brownian motion sources of risk, or a CIR model driven by one Brownian
motion source of risk. Both Heston and Bates models approximate continuous-time
stochastic processes by a quadratic-exponential discretization scheme. The
`simByQuadExp`

simulation derives directly from the
stochastic differential equation of motion; the discrete-time process approaches
the true continuous-time process only in the limit as
`DeltaTimes`

approaches zero.

`[`

specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.`Paths`

,`Times`

,`Z`

] = simByQuadExp(___,`Name,Value`

)

`[`

simulates `Paths`

,`Times`

,`Z`

,`N`

] = simByQuadExp(`MDL`

,`NPeriods`

)`NTrials`

sample paths of a Bates model driven by
two Brownian motion sources of risk, approximating continuous-time stochastic
processes by a quadratic-exponential discretization scheme. The
`simByQuadExp`

simulation derives directly from the
stochastic differential equation of motion; the discrete-time process approaches
the true continuous-time process only in the limit as
`DeltaTimes`

approaches zero.

[1] Andersen, Leif. “Simple and Efficient Simulation of the Heston Stochastic
Volatility Model.” *The Journal of Computational Finance* 11, no. 3
(March 2008): 1–42.

[2] Broadie, M., and O. Kaya. “Exact Simulation of Option Greeks under Stochastic
Volatility and Jump Diffusion Models.” In *Proceedings of the 2004 Winter
Simulation Conference*, 2004., 2:535–43. Washington, D.C.: IEEE,
2004.

[3] Broadie, Mark, and Özgür Kaya. “Exact Simulation of Stochastic Volatility and
Other Affine Jump Diffusion Processes.” *Operations Research* 54,
no. 2 (April 2006): 217–31.

`bates`

| `heston`

| `cir`

| `simByEuler`

| `simByTransition`