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Plotting Sensitivities of an Option
This example creates a three-dimensional plot showing how gamma changes relative to price for a Black-Scholes option. Recall that gamma is the second derivative of the option price relative to the underlying security price. The plot shows a three-dimensional surface whose z-value is the gamma of an option as price (x-axis) and time (y-axis) vary. It adds yet a fourth dimension by showing option delta (the first derivative of option price to security price) as the color of the surface. This example M-file is ftgex2.m.
Range = 10:70; Span = length(Range); j = 1:0.5:12; Newj = j(ones(Span,1),:)'/12;For each time period create a vector of prices from 10 to 70 and create a matrix of all ones.
JSpan = ones(length(j),1); NewRange = Range(JSpan,:); Pad = ones(size(Newj));Call the toolbox gamma and delta sensitivity functions. Exercise price is $40, risk-free interest rate is 10%, and volatility is 0.35 for all prices and periods. Gamma is the z-axis, delta is the color.
ZVal = blsgamma(NewRange, 40*Pad, 0.1*Pad, Newj, 0.35*Pad); Color = blsdelta(NewRange, 40*Pad, 0.1*Pad, Newj, 0.35*Pad);Draw the surface as a mesh, add axis labels and a title. The axes range from 10 to 70, 1 to 12, and -
to .
mesh(Range, j, ZVal, Color);
xlabel('Stock Price ($)');
ylabel('Time (months)');
zlabel('Gamma');
title('Call Option Sensitivity Measures');
axis([10 70 1 12 -inf inf]);
Finally add a box around the whole plot, annotate the colors with a bar, and label the colorbar.
set(gca, 'box', 'on');
colorbar('horiz');
a = findobj(gcf, 'type', 'axes');
set(get(a(2), 'xlabel'), 'string', 'Delta');
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