Thursday, August 21, 2008

Monte Carlo Simulation

What is it?

If you look up Monte Carlo Simulation on Investopedia: A problem solving technique used to approximate the probability of certain outcomes by running multiple trial runs, called simulations, using random variables.

That does not necessarily mean anything to me other than it uses statistics to solve a problem. The question for traders is: What problem does it solve and how do I implement a Monte Carlo Simulation?

PROBLEM:

Let's say that you have designed an optimized trading system. You want to know the likelihood of the systems success over a certain time period (presumably into the future). This is what the Monte Carlo Simulation (MCS from now on) can do for you. This technique has been used for several decades by trading companies (notably Long Term Capital Management) to model options valuations and potential trading performance.

IMPLEMENTATION:

An MCS can be designed quickly in Excel or built in any programming language. I use Excel because my non VBA skills are a little lacking and the simulations that I perform are generally not overly complex. For trading applications an MCS requires the following variables:

% winning trades
average or median return of winners
(standard deviation of winning returns)
% losing trades
average or median return of losers
(standard deviation of losing returns)

These statistics can be calculated over daily, weekly, monthly, etc. bars. Standard deviation is not necessary, but it does create more randomness which enhances the simulation's value.

(Continued on a later day)

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