## Pricing a Spread Option in MATLAB

A Spread option is an example of an option that has a payoff that is both path dependent and is dependent on multiple assets. This makes it ideally suited for pricing using the Monte-Carlo approach as discussed in the Monte-Carlo Methods tutorial.

The Simulating Multiple Asset Paths in MATLAB tutorial gives an example of a MATLAB function for generating the types of correlated multiple asset paths required for option pricing using Monte-Carlo methods. That tutorial is expanded here where MATLAB code for pricing a Spread option is presented.

The following is code for generating a user specified number of correlated asset paths for two assets and then using those paths to price a given Spread option. The payoff of the option is given by Equation 1: Payoff for a given Spread Option

where Δ(t)max is the maximum spread between the two assets over the lifetime of the option and Δallowable is a constant pre-specified maximum allowable spread.

```% Script to price a spread option using a monte-carlo approach
% Some parts of this could be vectorized, but has not been done here
% so that it's easier to understand what's going on.

% Define required parameters
S0 = [50 52];
r = 0.02;
mu = [0.03 0.04];
sig = [0.1 0.15];
corr = [1 0;0 1];
dt = 1/365;
etime = 50; % days to expiry
T = dt*etime;

nruns = 100000;

% generate the paths
S = AssetPathsCorrelated(S0,mu,sig,corr,dt,etime,nruns);

% The payoff is path dependent
payoff = nan*ones(nruns,1);
for idx = 1:nruns
maxDifference = diff(squeeze(S(:,idx,:)),1,2);
payoff(idx) = 0;
else
end
end

% Determine the option price
oPrice = mean(payoff)*exp(-r*T)
```

### Example Usage

The following shows the results of executing the Spread script.

```oPrice =
1.3074
```

Other MATLAB based Monte-Carlo tutorials are linked off the Software Tutorials page.