Analytic value function for a pairs trading strategy with a Lévy-driven Ornstein–Uhlenbeck process

This paper studies the performance of pairs trading strategy under a specific spread model. Based on the empirical evidence of mean reversion and jumps in the spread between pairs of stocks, we assume that the spread follows a Lévy-driven Ornstein–Uhlenbeck process with two-sided jumps. To evaluate the performance of a pairs trading strategy, we propose the expected return per unit time as the value function of the strategy. Significantly different from the current related works, we incorporate an excess jump component into the calculation of return and time cost. Further, we obtain the analytic expression of strategy value function, where we solve out the probabilities of crossing thresholds via the Laplace transform of first passage time of the Lévy-driven Ornstein–Uhlenbeck process in one-sided and two-sided exit problems. Through numerical illustrations, we calculate the value function and optimal thresholds for a spread model with symmetric jumps, reveal the non-negligible contribution of incorporating the excess jumps into the value function, and analyze the impact of model parameters on the strategy performance.     

Exploiting social media with higher-order Factorization Machines: statistical arbitrage on high-frequency data of the S&P 500

Over the past 15 years, there have been a number of studies using text mining for predicting stock market data. Two recent publications employed support vector machines and second-order Factorization Machines, respectively, to this end. However, these approaches either completely neglect interactions between the features extracted from the text, or they only account for second-order interactions. In this paper, we apply higher-order Factorization Machines, for which efficient training algorithms have only been available since 2016. As Factorization Machines require hyperparameters to be specified, we also introduce a novel adaptive-order algorithm for automatically determining them. Our study is the first one to make use of social media data for predicting minute-by-minute stock returns, namely the ones of the S&P 500 stock constituents. We show that, unlike a trading strategy employing support vector machines, Factorization-Machine-based strategies attain positive returns after transactions costs for the years 2014 and 2015. Especially the approach applying the adaptive-order algorithm outperforms classical approaches with respect to a multitude of criteria, and it features very favorable characteristics.     

Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns

This paper shows that occasional breaks generate slowly decaying autocorrelations and other properties of I(d) processes, where d can be a fraction. Some theory and simulation results show that it is not easy to distinguish between the long memory property from the occasional-break process and the one from the I(d) process. We compare two time series models, an occasional-break model and an I(d) model to analyze S&P 500 absolute stock returns. An occasional-break model performs marginally better than an I(d) model in terms of in-sample fitting. In general, we found that an occasional-break model provides less competitive forecasts, but not significantly. However, the empirical results suggest a possibility such that, at least, part of the long memory may be caused by the presence of neglected breaks in the series. We show that the forecasts by an occasional break model incorporate incremental information regrading future volatility beyond that found in I(d) model. The findings enable improvements of volatility prediction by combining I(d) model and occasional-break model.