Monday, May 13, 2013

Quasi Monte Carlo in Finance

I have been wondering if there was any better alternative than the standard Sobol (+ Brownian Bridge) quasi random sequence generator for the Monte Carlo simulations of finance derivatives.

Here is what I found:
  1. Scrambled Sobol. The idea is to rerandomize the quasi random numbers slightly. It can provide better uniformity properties and allows for a real estimate of the standard error. There are many ways to do that. The simple Cranley Patterson rotation consisting in adding a pseudo random number modulo 1, Owen scrambling (permutations of the digits) and simplifications of it to achieve a reasonable speed. This is all very well described in Owen Quasi Monte Carlo document
  2. Lattice rules. It is another form of quasi random sequences, which so far was not very well adapted to finance problems. A presentation from Giles & Kuo look like it's changing.
  3. Fast PCA. An alternative to Brownian Bridge is the standard PCA. The problem with PCA is the performance in O(n^2). A possible speedup is possible in the case of a equidistant time steps. This paper shows it can be generalized. But the data in it shows it is only advantageous for more than 1024 steps - not so interesting in Finance.


  1. Just wanna say:"




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    Damn... wow.

  2. What an irrelevant comment. I just stumbled on your blog and I think it's top notch.