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Example 7: A 3D plot

We will make a plot of the second partial derivative of the GarmanKohlhagen theoretical price of a European put option with respect to the spot price, as a function of exercise and spotprice. The spot price and the exercise price are varied between 80 and 120, the domestic and the foreign spot interest rates are assumed to be constant at 10 percent, and the volatility is 25 percent per year.

Load the DerivativesExpert`Options` package and the DerivativesExpert`GarmanKohlhagen` package from within Excel.

The function is entered in an Excel cell as:

=Math("Plot3D", "D[ EuropeanPutOption, GarmanKohlhagen[ x, y, 1/2, 10, 10, 25], {SpotPrice, 2}]", "{x, 80, 120}", "{y, 80, 120}", "PlotPoints -> 30", "PlotRange -> All", "ViewPoint -> {-1.3, -2.4, 2.0}", "AxesLabel -> {""spotprice"", ""exercise"", ""Gamma""}", "TextStyle->{FontSlant->""Italic"", FontSize->10}")

The 3D plot shows e.g. that gamma is greatest at-the-money.