{"id":3604,"date":"2012-02-06T19:49:38","date_gmt":"2012-02-06T18:49:38","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=3604"},"modified":"2015-10-07T16:49:51","modified_gmt":"2015-10-07T15:49:51","slug":"optimising-a-correlated-asset-calculation-on-matlab-1-vectorisation-on-the-cpu","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=3604","title":{"rendered":"Optimising a correlated asset calculation on MATLAB #1 – Vectorisation on the CPU"},"content":{"rendered":"

Recently, I’ve been working with members of The Manchester Business School<\/a> to help optimise their MATLAB<\/a> code. We’ve had some great successes using techniques such as vectorisation<\/a>, mex files<\/a> and The NAG Toolbox for MATLAB<\/a> (among others) combined with the raw computational power of Manchester’s Condor Pool<\/a> (which I help run along with providing applications support).<\/p>\n

A couple of months ago, I had the idea of taking a standard calculation in computational finance and seeing how fast I could make it run on MATLAB using various techniques. I’d then write these up and publish here for comment.<\/p>\n

So, I asked one of my collaborators, Yong Woong Lee, a doctoral researcher in the Manchester Business School, if he could furnish me with a very simple piece computational finance code. I asked for something that was written to make it easy to see the underlying mathematics rather than for speed and he duly obliged with several great examples. I took one of these examples and stripped it down even further to its very bare bones.\u00a0 In doing so I may have made his example close to useless from a computational finance point of view but it gave me something nice and simple to play with.<\/p>\n

What I ended up with was a simple piece of code that uses monte carlo techniques to find the distribution of two correlated assets: original_corr.m<\/a><\/p>\n

%ORIGINAL_CORR - The original, unoptimised code that simulates two correlated assets\r\n\r\n%% Correlated asset information\r\nCurrentPrice = [78 102];       %Initial Prices of the two stocks\r\nCorr = [1 0.4; 0.4 1];         %Correlation Matrix\r\nT = 500;                       %Number of days to simulate = 2years = 500days\r\nn = 100000;                    %Number of simulations\r\ndt = 1\/250;                    %Time step (1year = 250days)\r\nDiv=[0.01 0.01];               %Dividend\r\nVol=[0.2 0.3];                 %Volatility\r\n\r\n%%Market Information\r\nr = 0.03;                      %Risk-free rate\r\n\r\n%% Define storages\r\nSimulPriceA=zeros(T,n);    %Simulated Price of Asset A\r\nSimulPriceA(1,:)=CurrentPrice(1);\r\nSimulPriceB=zeros(T,n);    %Simulated Price of Asset B\r\nSimulPriceB(1,:)=CurrentPrice(2);\r\n\r\n%% Generating the paths of stock prices by Geometric Brownian Motion\r\nUpperTriangle=chol(Corr);    %UpperTriangle Matrix by Cholesky decomposition\r\n\r\nfor i=1:n\r\n   Wiener=randn(T-1,2);\r\n   CorrWiener=Wiener*UpperTriangle;\r\n   for j=2:T\r\n      SimulPriceA(j,i)=SimulPriceA(j-1,i)*exp((r-Div(1)-Vol(1)^2\/2)*dt+Vol(1)*sqrt(dt)*CorrWiener(j-1,1));\r\n      SimulPriceB(j,i)=SimulPriceB(j-1,i)*exp((r-Div(2)-Vol(2)^2\/2)*dt+Vol(2)*sqrt(dt)*CorrWiener(j-1,2));\r\n   end\r\nend\r\n\r\n%% Plot the distribution of final prices\r\n% Comment this section out if doing timings\r\n% subplot(1,2,1);hist(SimulPriceA(end,:),100);\r\n% subplot(1,2,2);hist(SimulPriceB(end,:),100);<\/pre>\n
On my laptop, this code takes 10.82 seconds<\/strong> to run on average.\u00a0 If you comment out the final two lines then it’ll take a little longer and will produce a histogram of the distribution of final prices.<\/p>\n
\"Two<\/p>\n
I’m going to take this code and modify it in various ways to see how different techniques and technologies can make it run more quickly. Here is a list of everything I have done so far.<\/p>\n