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Finance[DeterministicProcess] - create new deterministic process

 Calling Sequence DeterministicProcess(x, t)

Parameters

 x - procedure or algebraic expression; value function t - time variable

Description

 • The DeterministicProcess command creates a new deterministic process. The parameter x is the value of the process. The value can be constant or time-dependent and can be given either as an algebraic expression or a procedure. A procedure defining the value of a deterministic process must accept one argument (the time) and return the corresponding value of the process. If the value is given as an algebraic expression, it must depend on a single variable.

Examples

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $v:=\mathrm{piecewise}\left(t<1,t,\frac{1}{t}\right)$
 ${v}{:=}{{}\begin{array}{cc}{t}& {t}{<}{1}\\ \frac{{1}}{{t}}& {\mathrm{otherwise}}\end{array}$ (1)
 > $G:=\mathrm{DeterministicProcess}\left(v,t\right)$
 ${G}{:=}{\mathrm{_P}}$ (2)
 > $S:=\mathrm{SamplePath}\left(G\left(t\right),t=0..3,\mathrm{timesteps}=50\right)$
 ${S}{:=}\left[\begin{array}{c}{\mathrm{1..1 x 1..51}}{\mathrm{Array}}\\ {\mathrm{Data Type:}}{{\mathrm{float}}}_{{8}}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{C_order}}\end{array}\right]$ (3)
 > $\mathrm{plots}[\mathrm{display}]\left(\mathrm{PathPlot}\left(S,\mathrm{timegrid}=0..3,\mathrm{gridlines},\mathrm{thickness}=3,\mathrm{color}=\mathrm{blue}\right),\mathrm{plot}\left(v,t=0..3,\mathrm{thickness}=3,\mathrm{color}=\mathrm{red}\right)\right)$

References

 Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.
 Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

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