Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations

Algorithm 2

%  Cash-or-nothing options

clear;clc;clf;K=100;L=3*K;T=1;sigma=0.35;r=0.05;Nx=L+1;dt=0.01;Nt=round(T/dt);

x=linspace(0,L,Nx);h=x(2)-x(1);

for i=1:Nx

if (x(i) <= K)

payoff(i)=0.0;

else payoff(i)=1.0;

end

end

d=(log(x/K)+(r-sigma2/2)*T)/(sigma*sqrt(T));exact=1.0*exp(-r*T).*normcdf(d); grid on;

hold on;plot(x,payoff,‘k-’,x,exact, ‘r-’, ‘LineWidth’,1)axis ([0 300 -0.05 1.05])