Code covered by the BSD License

# American Monte Carlo

### Kienitz Wetterau FinModelling (view profile)

Algorithms for pricing American Style derivatives with Monte Carlo Simulation

barrier_bintree(S, df, p, K, Barrier, type)
```% This is material illustrating the methods from the book
% Financial Modelling  - Theory, Implementation and Practice with Matlab
% source
% Wiley Finance Series
% ISBN 978-0-470-74489-5
%
% Date: 02.05.2012
%
% Authors:  Joerg Kienitz
%           Daniel Wetterau
%
% kienitzwetterau_FinModelling@gmx.de
%
% (C) Joerg Kienitz, Daniel Wetterau
%
% Since this piece of code is distributed via the mathworks file-exchange
% it is covered by the BSD license
%
% This code is being provided solely for information and general
% illustrative purposes. The authors will not be responsible for the
% consequences of reliance upon using the code or for numbers produced
% from using the code.

function y = barrier_bintree(S, df, p, K, Barrier, type)
% prices an american barrier option using a binomial tree
n = size(S,2)-1;
v = cell(1, n+1);                               % option value

if type == 0
index = @(mval,x) mval > Barrier * ones(2^x,1);
payoff = @(x) max(x- K,0);
m_val = max(S,[],2);
else
index = @(mval,x) mval < Barrier * ones(2^x,1);
payoff = @(x) max(K-x,0);
m_val = min(S,[],2);
end

v{n+1} = index(m_val,n) .* payoff(S(:,end));

iVec = 1:length(S);
for i = n:-1:2
iVec = iVec(1:length(iVec)/2) * 2;

if type == 0
m_val = max(S(iVec,1:i),[], 2);
else
m_val = min(S(iVec,1:i),[], 2);
end
Jset = 1:2:2^i;
expected_val = p * v{i+1}(Jset) ...
+ (1-p) * v{i+1}(1+Jset) * df;           % cont value

v{i} = index(m_val,i-1) .* payoff(S(iVec,i));% current opt value
v{i}=max(v{i}, expected_val);                % option value at t_i

end

y = p * v{2}(1) * df + (1-p) * v{2}(2) * df;      % option value at t_0
end```