CODEWITHSUNDEEP
matlabcomplexity-theory
Babyburger
Babyburger

Reputation: 1830

speed up program execution [matlab]

I want to run the following .m file in matlab:

function [relativeErrors] = plotRelativeErrors()

initialPrice = 115.47;
sigma = 1.34*10^(-2);
tau = 0;
days = 40;
Strike = 114;

Time = days/365;
[callSol, ~] = blsprice(initialPrice, Strike, tau, Time, sigma);

termOne = (tau - (sigma^2)/2)*days;
termTwo = sigma * sqrt(days);

relativeErrors = [];
for i = 1:8
    max = 0;
    N = 10^i;
    for n = 1:50
        v = intern_eurValue(Strike, initialPrice, days, N, termOne, termTwo);
        difference = abs(v-callSol);

        if difference > max
            max = difference;
        end
    end
    relativeErrors(end+1) = max;
end

end


function [value] = intern_eurValue(strike, price, days, N, termOne, termTwo)

prices = intern_simulateEndPrice(price, termOne, termTwo, days, N);
theMean = mean(prices);
value = theMean - strike;

if value < 0
    value = 0;
end

end


function [prices] = intern_simPrice(initialPrice, termOne, termTwo, days, N)

prices = [];

for i = 1:N
    termTwo = termTwo * normrnd(0,1);
    exponential = exp(termOne + termTwo);
    prices(end+1,1) = initialPrice * exponential;
end

end

The problem is that running this will take over a day, if not more to complete calculating. I had to call it quits after it was running for 14 hours and wasn't halfway done. I have already tried to optimize runtime by delegating most of the computations that are static from intern_simPrice to plotRelativeErrors and passing the results through termOne and termTwo, but I barely notice any progression.

I don't think this can be reduced in terms of less computations, but perhaps it can be switched to something that would calculate faster.

Upvotes: 0

Views: 93

Answers (1)

knedlsepp
knedlsepp

Reputation: 6084

Disclaimer: The following approaches will help you reach usable speeds, but will not reduce the time complexity, per se.

If your computation is slow, first thing to do is to use the profiler to find out what's slowing you down. In your case its intern_simPrice and especially millions of calls to normrnd.

Fewer function calls:

It's usually a lot faster to let a function compute multiple values in one call. So, first thing you should replace:

for i = 1:N
    termTwo = termTwo * normrnd(0,1);
    ....
end

with

X_norm = normrnd(0,1,1,N); % Generate N random values simultaneously
for i = 1:N
    termTwo = termTwo * X_norm(i);
    ....
end

Preallocation:

If you know how long your arrays are going to be, it's also smarter to allocate them in advance. So you should replace:

prices = []
for i = 1:N
    prices(end+1) = ...

with

prices = zeros(N,1);
for i = 1:N
    prices(i) = ...

Vectorization:

Sometimes for loops can be replaced by a vectorized version. In your case this would be: Replacing the function intern_simPrice altogether and just using:

prices = initialPrice*exp(termOne + termTwo*cumprod(normrnd(0,1,N,1)));

Upvotes: 2

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