• #timeseries
• #gas
• #statisticalarbitrage
• #finance
• #trading

In 1985 while at Morgan Stanley, Nunzio Tartaglia and a small group of mathematicians, physicists, and computer scientists devised a trading algorithm that was able to generate enormous profits. The idea was extremely simple: find two assets whose price movements were similar and then bet on their divergences. This was the birth of pair trading that evolved in the broader field of statistical arbitrage in the following years. In time, the procedure adopted at Morgan Stanley became public and more and more investors started to exploit it. Since then the profitability of the statistical arbitrage strategies has declined, especially from the beginning of the new millennium. Hence, more complex models substituted the old and simple algorithm with the hope of better performances.

In this perspective, many methods of time series analysis can be exploited. In recent years, a new class of models have become popular to track the dynamics of time-varying parameters. They are called the Generalized Autoregressive Score driven models (GAS models). Their great flexibility, together with their optimality properties in an information-theoretic perspective, make them one of the first choices when the dynamics of a parameter is unknown.

In the present thesis, I generalize one of the most famous statistical arbitrage strategies: the one devised by Avellaneda and Lee and presented in their paper Statistical arbitrage in US equities market (2008). Firstly, I replicate the original strategy on new and more recent data. Then, through the implementation of GAS models, I filter the dynamics of one of the parameters assumed to be constant in the original strategy. \Specifically, Avellaneda and Lee's strategy uses an autoregressive process of order one to model the behaviour of the cointegration residuals. The parameter of this model is assumed to be constant. What I have argued is that the autoregressive coefficient experiences a non trivial dynamics.

The structure of the thesis is organized with the first two chapters and part of the third reviewing the existing literature. Then, using the previous discussions, the last chapters contain my original contribution, presenting my implementation of Avellaneda and Lee's strategy, the behaviour of GAS models and the use of them in the strategy.

The detailed structure of the present work is:


- In chapter 1 I contextualize historically the statistical arbitrage strategies. I present the main ideas on which they are based, with particular focus on the concept of overreaction in the stock market, the main results of Principal Component Analysis and Random Matrix Theory. These last two topics are useful in the creation of the strategy since they are able to create the appropriate set of risk factors by which trades are performed.

- In chapter 2 I illustrate Avellaneda and Lee's strategy. Based on stochastic processes, I explain the mathematics behind it and the results obtained by the authors. This discussion is fundamental to understand the different approaches that I adopted both in the application of this strategy to new data and in the GAS model implementation.

- In chapter 3 I present the general framework of GAS models. I explain the different sources of uncertainty that the filtering procedure carries. I focus my attention on the so-called parameter uncertainty and I illustrate three different methods to evaluate it. The GAS models are then specialized to the case of an autoregressive process of order one with a time-varying autoregressive parameter. Some examples on synthetic data are provided to check the behaviour of the GAS filter and the estimation procedure.


- In chapter 4 I implement Avellenda and Lee's strategy on new and more recent data (1995-2020) that I divided into a validation set (1995-2011) and a test set (2012-2020). The assumptions made by the authors are checked using different statistical tests like the Augmented-Dickey-Fuller test for stationarity, the D'Agostino and Pearson normality test and the Ljung-Box test on correlations. Moreover, the tuning of model hyperparameters is carried out more deeply on the validation set and the resulting model is applied to the test set. In the last section of this chapter, I present the outcome of the strategy on the test set. The generated profits experience a significant decline when compared to the results on the validation set, in accordance to the existing literature.

- In chapter 5 I modify the constructed strategy by implementing GAS models. The most important dynamics of the original model is an autoregressive process of order one. In this chapter, I reject the assumption of a constant autoregressive parameter based on the result of a Lagrange multiplier test. Hence, I filter its dynamics using GAS models. All the statistical tests done on the original strategy are performed again. The implementation of GAS models led to worse results than the case of constant autoregressive coefficient. The study of the outcomes of the filtering procedure suggests the reasons of this decline. Hence, I propose some possible ways to improve the performance of the new strategy.


- In chapter 6 the conclusions of this work are drawn and the major results are summarized. Particular attention is then put on the limits of the models and on the possible ways to improve them, both from the perspective of more realism and better performance.