output = discount or zerorate; output type

The DiscountBondPrice command calculates the discount bond price in the given affine interest rate model.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$M≔\mathrm{VasicekModel}\left(0.05\,0.03\,0.5\,0.03\right)$

$M≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$X≔\mathrm{ShortRateProcess}\left(M\right)$

$X≔\mathrm{\_X0}$

$T≔\left[\mathrm{seq}\left(0.6i\,i=0..50\right)\right]$

$T≔\left[0.\,0.6\,1.2\,1.8\,2.4\,3.0\,3.6\,4.2\,4.8\,5.4\,6.0\,6.6\,7.2\,7.8\,8.4\,9.0\,9.6\,10.2\,10.8\,11.4\,12.0\,12.6\,13.2\,13.8\,14.4\,15.0\,15.6\,16.2\,16.8\,17.4\,18.0\,18.6\,19.2\,19.8\,20.4\,21.0\,21.6\,22.2\,22.8\,23.4\,24.0\,24.6\,25.2\,25.8\,26.4\,27.0\,27.6\,28.2\,28.8\,29.4\,30.0\right]$

$S≔\mathrm{SamplePath}\left(X\left(t\right)\,t=0..1\,\mathrm{timesteps}=50\right)$

$\mathrm{PathPlot}\left(S\,\mathrm{thickness}=3\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

$P≔\mathrm{seq}\left(\mathrm{Statistics}\left[\mathrm{LineChart}\right]\left(\mathrm{DiscountBondPrice}\left(M\,S\left[1,i\right]\,T\,\mathrm{output}=\mathrm{zerorate}\right)\,\mathrm{xcoords}=T\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{thickness}=3\,\mathrm{markers}=\mathrm{false}\right)\,i=1..51\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(P\,\mathrm{insequence}=\mathrm{true}\right)$

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York: Springer-Verlag, 2001.

The Finance[DiscountBondPrice] command was introduced in Maple 15.

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