Aug
24

## PSOR for American option

We often have to price the American Option with Linear Complementarity Formulation when using finite difference method. One of methods for solving linear complementarity problem is

x'(Ax - b) = 0

x >= 0

Ax - b >= 0

using the

function [x] = psor(A,b,x0)

omega = 1.5;

tol = 1e-9;

jmax = 1e+3;

n = length(b); x = x0; j = 1;

for i = 1:n

x(i) = max(0,x(i)+omega*(b(i)-A(i,:)*x)/A(i,i));

end

while (norm(x-x0) > tol) && (j < jmax)

j = j + 1; x0 = x;

for i = 1:n

x(i) = max(0,x(i)+omega*(b(i)-A(i,:)*x)/A(i,i));

end

end

return

A problem with this sample code is slow computation speed, Should you are happy with C++, the following C++ code which can be called directly in Matlab.

wiki(Linear complementarity problem)

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Optimization packages

**Projected Successive Over Relaxation (PSOR)**, which is iterative and tries to solve the following formulation:x'(Ax - b) = 0

x >= 0

Ax - b >= 0

using the

**projected SOR**algorithm. Here is a sample Matlab code showing the basic algorithem of**PSOR**,function [x] = psor(A,b,x0)

omega = 1.5;

tol = 1e-9;

jmax = 1e+3;

n = length(b); x = x0; j = 1;

for i = 1:n

x(i) = max(0,x(i)+omega*(b(i)-A(i,:)*x)/A(i,i));

end

while (norm(x-x0) > tol) && (j < jmax)

j = j + 1; x0 = x;

for i = 1:n

x(i) = max(0,x(i)+omega*(b(i)-A(i,:)*x)/A(i,i));

end

end

return

A problem with this sample code is slow computation speed, Should you are happy with C++, the following C++ code which can be called directly in Matlab.

Download

wiki(Linear complementarity problem)

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