Algorithms for pricing American Style derivatives with Monte Carlo Simulation
BinTree_CP(S0, K, r, T, sigma, n, 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
%
% Please send comments, suggestions, bugs, code etc. to
% 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 = BinTree_CP(S0, K, r, T, sigma, n, type)
% American call/put pricing using a binomial tree
% S0: Spot value
% K: Strike
% r: riskless rate
% T: Maturity
% sigma: volatility
% n: periods for tree
% type: 0 put, 1 call
dt = T / n; % length of one period
u = exp(sigma * sqrt(dt)); % up move
d = 1 / u; % down move
D = exp(-r * dt); % discount
p = (1/D - d) / (u - d); % probability
S{n} = S0 * u^n * d.^(0:2:2*n);
if type == 0
cp = 1;
else
cp = -1; % payoff at t_N
end
v{n} = max(cp*(S{n}-K), 0); % payoff at t_N
for i = n-1:-1:1
S{i} = S0 * u.^i * d.^(0:2:2*i);
v{i} = max(cp*(S{i}-K), 0);
expected_val = p * v{i+1}(1:end-1) * D ...
+ (1-p) * v{i+1}(2:end) * D; % expected value of price
index = v{i} < expected_val; % early exercise or not
v{i}(index) = expected_val(index); % value at t_i
end
y = p * v{1}(1) * D + (1-p) * v{1}(2) * D; % option value t_0
end