bs.m

function bs
%BS    Black-Scholes PDE.
%   Solves the transformed Black-Scholes equation.

m = 0;
r = 0.065;
sigma = 0.8;
k = r/(0.5*sigma^2);
a = log(2/5);
b = log(7/5);
t0 = 0;
tf = 5;

xmesh = linspace(a,b,40);
tspan = linspace(t0,tf,20);

sol = pdepe(m,@bspde,@bsic,@bsbc,xmesh,tspan);
u = sol(:,:,1);

mesh(xmesh,tspan,u)
xlabel('x','FontSize',12)
ylabel('t','FontSize',12)
zlabel('u','FontSize',12,'Rotation',0)
colormap copper

    function [c,f,s] = bspde(x,t,u,DuDx)
    %BSPDE    Black-Scholes PDE.
    c = 1;
    f = DuDx;
    s = (k-1)*DuDx-k*u;
    end

    function u0 = bsic(x)
    %BSIC   Initial condition at t = t0.
    u0 = max(exp(x)-1,0);
    end

    function [pa,qa,pb,qb] = bsbc(xa,ua,xb,ub,t)
    %BSBC   Boundary conditions at x = a and x = b.
    pa = ua;
    qa = 0;
    pb = ub - (7 - 5*exp(-k*t))/5;
    qb = 0;
    end

end