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Simulate approximate solution of diagonal-drift Merton jump diffusion process

`[`

simulates `Paths`

,`Times`

,`Z`

,`N`

] = simBySolution(`MDL`

,`NPeriods`

)`NNTrials`

sample paths of `NVars`

correlated state variables 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 Merton
jump diffusion process by an approximation of the closed-form solution.

The `simBySolution`

function simulates the state vector
*X _{t}* by an approximation of the
closed-form solution of diagonal drift Merton jump diffusion models. Specifically, it
applies a Euler approach to the transformed

`log`

[This function simulates any vector-valued `merton`

process of the
form

$$d{X}_{t}=B(t,{X}_{t}){X}_{t}dt+D(t,{X}_{t})V(t,{x}_{t})d{W}_{t}+Y(t,{X}_{t},{N}_{t}){X}_{t}d{N}_{t}$$

Here:

*X*is an_{t}`NVars`

-by-`1`

state vector of process variables.*B*(*t*,*X*_{t}) is an`NVars`

-by-`NVars`

matrix of generalized expected instantaneous rates of return.

is an*D*(*t*,*X*_{t})`NVars`

-by-`NVars`

diagonal matrix in which each element along the main diagonal is the corresponding element of the state vector.

is an*V*(*t*,*X*_{t})`NVars`

-by-`NVars`

matrix of instantaneous volatility rates.*dW*_{t}is an`NBrowns`

-by-`1`

Brownian motion vector.

is an*Y*(*t*,*X*_{t},*N*_{t})`NVars`

-by-`NJumps`

matrix-valued jump size function.*dN*_{t}is an`NJumps`

-by-`1`

counting process vector.

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[3] Glasserman, Paul.
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[4] Hull, John C.
*Options, Futures and Other Derivatives*. 7th ed, Prentice
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Statistics. New York: Wiley, 1995.

[6] Shreve, Steven E.
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2004.