Financial Simulation Modeling in Excel

QUASI–MONTE CARLO AND COMPUTATIONAL TIME

While the most direct ways to reduce the computational time of a model are to speed up the processing or write the program in a faster language, there are additional methods that can be used to reduce the number of runs that need to be done to get meaningful results. Speed can have a real impact on the ability to react to changing market conditions and execute trades. In some markets, minutes or seconds can be crucial in the capturing the value from news or new pricing data.

Most of the work on speeding up models that we will cover relates to Monte Carlo simulations, and the methods of analysis using these methods are called quasi–Monte Carlo methods. In these methods we take sequences of numbers for our draws that would appear to be random but that are in fact not random. The sequences are specifically designed to appear random and to be more efficient at covering a range of possible outcomes than a random sequence.

The simplest of these methods is the Halton sequence. The Halton sequence is constructed by choosing a prime number as a base, and then creating nonrandom draws up to the desired number of runs. Draws can also be across multiple dimensions; price, interest rates, the state of the economy, and the recovery rate of a bond may all be simulated together. However, Halton sequences are generally not used for more than five or six variables at a time due to loss of some of the properties of randomness.