Vectorisation of for loops

Being fairly new to Matlab and the concept of vectorisation rather than iteration I need some help getting my head around avoiding for loops.

I'd like to use arrayfun but don't know how to implement it with changing parameter dimensions.

Nested for loop

for k = 1:Sims
    for i = 1:Days
        Hist = sum(Weights(1:i,1) .* FF(1:i,k));
        Deltas(i,k) = Delta(FF(i,k), Hist, v(i:end), 60.64633, Weights(i:Days), 2500, Days-i);
    end
end

Notice that v and Weights dimensions decreases as i increases, and the last parameter passed to Delta (Days) is decreased in size by i.

Any thoughts, can it even be done?

[Matt Fig]

w and Weights do not change sizes in the loop. What is Sims and Days? And what is Delta?

Whether it is worthwhile to vectorize this will depend on these two values and what Delta is.

[Alex Gregory]

Delta approximates the value of Delta for an Asian option. It does this for i=1 to Days=(3*365) over k=1 to Sims=1000.

As i increases 1 day less of volatility and daily weightings are needed for the calculation as there are Days-i days remaining until the option expires.

[Jan]

@Alex: A cute answer. The meaning of the values is not important, only the type and size or if it is an array or a function. :-)

Answer 1

[Sean de Wolski]

arrayfun is slow and difficult to use/read. It has really no advantages. I do not know why you would want to use it over the for-loops. If you preallocate Deltas that will help with speed. Using arrayfun will hurt and make your code harder to understand.

Before the loop:

Deltas = zeros(Sims,Days)

Answer 2

[Jan]

At least calculating the sum repeatedly can be avoided:

Deltas = zeros(Days, Sims);
for k = 1:Sims
  Hist = cumsum(Weights(:, 1) .* FF(:, k));
  for ii = 1:Days
     Deltas(ii,k) = Delta(FF(i,k), Hist(ii), v(ii:end), 60.64633, Weights(ii:Days), 2500, Days-ii);
  end
end

If you post the code of "Delta" further improvements are possible.

[Alex Gregory]

function [ Delta ] = Delta( UnderlyingPrice, Hist, Vols, k, weights, sims, days)

      l = size(Vols,1);
      er = exp(-0.01*days/365);
      b = 0.001;
      t = 1/365;

      FFa = repmat(-0.5.*Vols.^2.*t,1,sims);
      Rands = randn(l,sims);
      FFb = repmat(Vols.*sqrt(t),1,sims) .* Rands;
      FF = exp(FFa+FFb);
      UL = repmat(UnderlyingPrice,l,sims);
      ULB = repmat(UnderlyingPrice+b,l,sims);
      W = repmat(weights,1,sims);
      FFCP = cumprod(FF);

      FCNB = FFCP .* UL .* W;

      FCNB = sum(FCNB) + Hist;

      FCNBPo = max(0,FCNB-k)*er;

      FCB = FFCP .* ULB .* W;
      FCB = sum(FCB) + Hist;
      FCBPo = max(0,FCB-k)*er;

      FF = exp(FFa-FFb);
      FFCP = cumprod(FF);
      FCatNB = FFCP .* UL .* W;
      FCatNB = sum(FCatNB) + Hist;
      FCatNBPo = max(0,FCatNB-k)*er;

      FCatB = FFCP .* ULB .* W;
      FCatB = sum(FCatB) + Hist;
      FCatBPo = max(0,FCatB-k)*er;

      Delta = mean(((FCBPo-FCNBPo) ./ b + (FCatBPo-FCatNBPo) ./ b) ./ 2);
  end

[Jan]

Obviously the main part of the program happens inside the function Delta(). Then the outer loop is most likely negligible.

If you provide some sample data, e.g. created by RAND(), such that we can tun your program, it would be easier to test modifications. I assume the REPMAT waste a lot of time here and some BSXFUN would be remarkably faster.

[Sean de Wolski]

That would be my first recommendation: replace every repmat with the corresponding bsxfun.