 DeterministicProcess - Maple Help

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}{≔}\left\{\begin{array}{cc}{t}& {t}{<}{1}\\ \frac{{1}}{{t}}& {\mathrm{otherwise}}\end{array}\right\$ (1)
 > $G≔\mathrm{DeterministicProcess}\left(v,t\right)$
 ${G}{≔}{\mathrm{_P}}$ (2)
 > $S≔\mathrm{SamplePath}\left(G\left(t\right),t=0..3,\mathrm{timesteps}=50\right)$
 ${S}{≔}\begin{array}{c}\left[\begin{array}{ccccccccccc}{0.}& {0.0600000000000000}& {0.120000000000000}& {0.180000000000000}& {0.240000000000000}& {0.300000000000000}& {0.360000000000000}& {0.420000000000000}& {0.480000000000000}& {0.540000000000000}& {\dots }\end{array}\right]\\ \hfill {\text{1 × 51 Array}}\end{array}$ (3)
 > $\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{PathPlot}\left(S,\mathrm{timegrid}=0..3,\mathrm{gridlines},\mathrm{thickness}=3,\mathrm{color}=\mathrm{blue}\right),\mathrm{plot}\left(v,t=0..3,\mathrm{thickness}=3,\mathrm{color}=\mathrm{red}\right)\right)$  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. Compatibility

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