Quant Report: Monte Carlo Simulations in Algorithmic Trading

Marc Leen, Samen Polishchuk

In the scope of algorithmic trading, we can design Monte Carlo simulations for forecasting algorithms and backtesting data. In this paper we will explain the mechanisms behind Monte Carlo simulations alongside investigating a simple algorithm for both cases of forecasting and backtesting data.

The paper covers the premise of Monte Carlo simulations, using a modification of Barbier’s solution to Buffon’s Needle Problem to calculate the value of pi, providing a simple proof of the advantages of repeated random sampling. We further create a Monte Carlo forecasting algorithm, for a portfolio of Apple (AAPL), Google (GOOGL), and Tesla (TSLA), testing the application of such an algorithm and its constraints. The forecasting algorithm should be based on a back data set that is necessarily short such that it would accurately describe the stock movement in the short-term forecast period.

We then develop and analyse a backtesting algorithm in this paper and demonstrate a few ways in which the algorithm can be used. Lastly, we explore a more complex form, Multi Level Monte Carlo (MLMC) simulations, in the extension section 5. This outlines a detailed explanation of how we can construct and implement MLMC simulations, touching on the ideas of variance reduction, computational complexity, and scalability.