Algorithmic Finance

We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market dynamics which we study both empirically and theoretically. We demonstrate that this model replicates observed market behavior on all relevant timescales (from days to years) reasonably well. Using the model, we obtain and discuss a number of results that pose implications for current market theory and offer potential practical applications.

This paper develops a new performance measurement methodology for algorithmic trading. By adapting capability from the quality control literature, we present new criteria for assessing control, expected tail loss and risk-adjusted performance in a single framework. The multi-scale capability measure we present is more descriptive and more appropriate for algorithmic trading than the traditional measure used in finance. It is robust to non-normality and the multiple time horizon decision processes inherent in algorithmic trading. We also argue that an algorithmic trading strategy, indeed any investment strategy, which satisfies the criteria to be multi-scale capable also satisfies any definition of prudence. It will be unlikely to harm the investor or external market participants in the event of its failure, while providing a high likelihood of satisfactory risk-adjusted performance.

The microstructural approach to the exchange rate market claims that order flows on a currency can accurately reflect the short-run dynamics of its exchange rate. In this paper, instead of focusing on order flows analysis we employ an alternative microstructural approach: We focus on investors' sentiment on a given exchange rate as a possible predictor of its future evolution. As a proxy of investors' sentiment we use StockTwits posts, a message board dedicated to finance. Within StockTwits investors are asked to explicitly state their market expectations. We collect daily data on the nominal exchange rate of four currencies against the U.S. dollar and the extracted market sentiment for the year 2013. Employing econometric and machine learning methodologies we develop models that forecast in out-of-sample exercise the future direction of the four exchange rates. Our empirical findings reject the Efficient Market Hypothesis even in its weak form for all four exchange rates. Overall, we find evidence that investors' sentiment as expressed in public message boards can be an additional source of information regarding the future directional movement of the exchange rates to the ones proposed by economic theory.

We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order risk.

We present a new method to measure the intraday relationship between movements of implied volatility smiles and stock index returns. It exploits a specific characteristic of the smile profile in high-frequency data. Using transaction data for EuroStoxx 50 options from 2000 to 2011 and DAX options from 1995 to 2011 (14 million transactions), we find that the intraday evolution of volatility smiles is generally not consistent with traders' rules of thumb such as the sticky strike or sticky delta rule. On average, the impact of index return on implied volatility is 1.3 to 1.5 times stronger than the sticky strike rule predicts. The main factor driving variations of the adjustment factor is the index return. Our results have implications for option valuation, hedging and the understanding of the leverage effect.