An Extension of the Monte Carlo Method

  •  Client: Econoinvest Casa de Bolsa
  • Date completed: 2010
  • Project description / goal: this was part of my thesis to obtain my master’s degree in Finance. One of Monte Carlo method’s uses consists on generating random data that replicate any original data series, for example, historical pricing data from financial instruments. The classical way to achieve this is to replicate the linear and colinear properties inherent in the original data series. However, this process is leaving out the nonlinear properties of such series. The project’s goal was to consider both the linear and nonlinear properties of the data during its replication.
  • My contribution: Monte Carlo’s method way of replicating data was enhanced by developing an extension which exploits the entropy and coentropy of the original data series. Such statistical properties were considered together with the linear properties of the data, such as correlation, standard deviation and probability distribution. This way, data being even closer statistically to the original one could be generated. This extension was done entirely by using Matlab.
  • Results: this improved method of replicating data has two direct benefits:
    • The backtesting of expert automated trading agents can now be done not only against the data series that actually occurred, but also against thousands of instances of the same data series, which has been replicated also non-linearly. This way backtesting can be taken to a new rigorous level filtering higher quality trading agents.
    • The Monte Carlo method of calculating the VaR (Value at Risk) of investment portfolios can also directly benefit from this. In order to calculate the VaR, series of data are generated to replicate the actual historical pricing data from the securities conforming the portfolio under analysis. If the data is generated even more realistically, then the VaR measurement can have increased precision.

A paper regarding Entropy and Coentropy

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