## Options Greeks – Matlab Code

In this Matlab code, we provide graphs of options Greeks as functions of the initial stock price. The Greeks provide useful information on the sensitivity of an option’s price over multiple factors. In this example, we include delta, theta, vega, rho and gamma.

function greeks(S1, S2, X, r, sigma, T)
echo off;
S0 = S1 : S2;

% plot delta
subplot(3,2,1);
d1 = (log(S0./X) + (r + 0.5 * (sigma.^2)).*T )./ (sigma.*sqrt(T));
d2 = d1 - sigma.*T;
bsc1 = S0.* normcdf(d1) - X.* exp(-r.* T).* normcdf(d2);
bsc2 = (S0.* normcdf(d1) + 0.01 * normcdf(d1)) - X.* exp(-r.* T).* normcdf(d2);
delta2 = (bsc2 - bsc1) / 0.01;
plot(S0, delta2);
title('Black-Scholes delta');

% plot theta
subplot(3,2,2);
d1=(log(S0./X) + (r + 0.5 * (sigma.^2)).*T )./ (sigma.*sqrt(T));
d2 = d1 - sigma.*T;
c1=0.5*sigma.*S0.*normpdf(d1)./sqrt(T);
c2=X.*r.*exp(-r.*T).*normcdf(d2);
theta = c1 + c2;
plot(S0, theta);
title('Black-Scholes theta');

% plot vega
subplot(3,2,3);
d1=(log(S0./X) + (r + 0.5 * (sigma.^2)).*T )./ (sigma.*sqrt(T));
vega = S0.*normpdf(d1).*sigma.*sqrt(T);
plot(S0,vega);
title('Black-Scholes vega');

% plot rho
subplot(3,2,4);
d1=(log(S0./X) + (r + 0.5 * (sigma.^2)).*T )./ (sigma.*sqrt(T));
d2 = d1 - sigma.*T;
rho = X.*T.*exp(-r.*T).*normcdf(d2);
plot(S0,rho);
title('Black-Scholes rho');

% plot gamma
subplot(3,2,5);
d1=(log(S0./X) + (r + 0.5 * (sigma.^2)).*T )./ (sigma.*sqrt(T));
gamma = normpdf(d1)./(S0.*sigma.*sqrt(T));
plot(S0,gamma);
title('Black-Scholes gamma');

echo on;