Financial Modeling in Maple 15 - Maple Programming Help

Financial Modeling in Maple 15

Finance Package for Financial Modeling and Personal Finance

 • The Finance package is new in Maple 15. This package offers functions for personal finance and advanced financial modeling. Parts of this package existed as the Maple Financial Modeling Toolbox before.
 • Areas of coverage:
 – Term structures and interest rates
 – Stochastic processes
 – Lattice methods
 – Calendars and day counters
 – Financial instruments such as European, American, and Bermudan options
 – Cash flow analysis
 – Short rate models
 – Personal finance

Examples

If you would like to receive 100 units of money each year for 20 years (for, say, a retirement package), you need less than $2000$ units to start with, because interest is paid (and compounds) over the sum that will be paid to you later. The amount needed can be computed by the annuity function. The following shows the result for an interest rate of 4%.

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{amount}≔\mathrm{annuity}\left(100,0.04,20\right)$
 ${\mathrm{amount}}{≔}{1359.032634}$ (1)

In order to model stock prices and volatility, financial modelers use many variations of different stochastic processes. One of these is the Merton Jump Diffusion process, demonstrated below. We generate 5 realizations of a particular Merton Jump Diffusion process.

 > $X≔\mathrm{MertonJumpDiffusion}\left(100,0.5,0.05,0.01,0.2,0.,0.5\right):$
 > $\mathrm{PathPlot}\left(X\left(t\right),t=0..1,\mathrm{timesteps}=100,\mathrm{replications}=5,\mathrm{color}=\mathrm{red}..\mathrm{blue},\mathrm{thickness}=3,\mathrm{axes}=\mathrm{BOXED},\mathrm{gridlines}=\mathrm{true}\right)$