## Monte Carlo simulation

Posted by alifinmath on February 7, 2008

Monte Carlo simulation is one of the key instruments in any quant’s arsenal of tools and techniques. A self-respecting quant program should have at least one semester devoted entirely to Monte Carlo methods. The key topics in such a course could be:

1) Generating randon variables by inverse transform and by acceptance-rejection.

2) Methods for generating pseudo-random numbers and their statistical properties (so that at least one is aware of what’s taking place under the bonnet of programs such as MatLab and Excel).

3) Naive (i.e., “independent”) Monte Carlo methods, used for purposes such as evaluating integrals.

4) Variance-reduction methods

5) Markov-Chain Monte Carlo (time permitting).

It’s not just that lecturing on these topics takes time: it’s that developing any sort of skill using these ideas takes time and practice with lots of examples and problems.

Monte Carlo has its genesis in physics. A paper sketching the early development of MC can be found here. Among books, the three introductory treatments I’ve found — in roughly increasing order of difficulty — are:

1) Simulation, Fourth Edition, by Sheldon Ross,

2) A First Course in Monte Carlo, by George Fishman, and

3) Monte Carlo Statistical Methods (Springer Texts in Statistics), by Robert and Casella

As usual, the Springer book is the best value for money (American publishers are heartless bandits). The international version of the Ross book can be found for about $30. In addition it’s the most accessible book, with lots of intuitive explanations and illustrative examples. I’ll try to write brief reviews of these books in the sister blog, Quant Book Reviews, in the next few days.

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