High performance digital signal processing: Theory, design, and applications in finance

The way scientific research and business is conducted has drastically changed over the last decade. Big data and data-intensive scientific discovery are two terms that have been coined recently. They describe the tremendous amounts of noisy data, created extremely rapidly by various sensing devices and methods that need to be explored for information inference. Researchers and practitioners who can obtain meaningful information out of big data in the shortest time gain a competitive advantage. Hence, there is more need than ever for a variety of high performance computational tools for scientific and business analytics. Interest in developing efficient data processing methods like compression and noise filtering tools enabling real-time analytics of big data is increasing. A common concern in digital signal processing applications has been the lack of fast handling of observed data. This problem has been an active research topic being addressed by the progress in analytical tools allowing fast processing of big data. One particular tool is the Karhunen-Loève transform (KLT) (also known as the principal component analysis) where covariance matrix of a stochastic process is decomposed into its eigenvectors and eigenvalues as the optimal orthonormal transform. Specifically, eigenanalysis is utilized to determine the KLT basis functions. KLT is a widely employed signal analysis method used in applications including noise filtering of measured data and compression. However, defining KLT basis for a given signal covariance matrix demands prohibitive computational resources in many real-world scenarios. In this dissertation, engineering implementation of KLT as well as the theory of eigenanalysis for auto-regressive order one, AR(1), discrete stochastic processes are investigated and novel improvements are proposed. The new findings are applied to well-known problems in quantitative finance (QF). First, an efficient method to derive the explicit KLT kernel for AR(1) processes that utilizes a simple root finding method for the transcendental equations is introduced. Performance improvement over a popular numerical eigenanalysis algorithm, called divide and conquer, is shown. Second, implementation of parallel Jacobi algorithm for eigenanalysis on graphics processing units is improved such that the access to the dynamic random access memory is entirely coalesced. The speed is improved by a factor of 68.5 by the proposed method compared to a CPU implementation for a square matrix of size 1,024. Third, several tools developed and implemented in the dissertation are applied to QF problems such as risk analysis and portfolio risk management. In addition, several topics in QF, such as price models, Epps effect, and jump processes are investigated and new insights are suggested from a multi-resolution (multi-rate) signal processing perspective. It is expected to see this dissertation to make contributions in better understanding and bridging the analytical methods in digital signal processing and applied mathematics, and their wider utilization in the finance sector. The emerging joint research and technology development efforts in QF and financial engineering will benefit the investors, bankers, and regulators to build and maintain more robust and fair financial markets in the future

Machine Learning in Finance: Estimation, Inference and Financial Applications for Correlated Data

Modern technologies have generated big data at an unprecedented scale and speed, which has spurred remarkable progress in high-dimensional statistical research and o ers alternative solutions to some prominent nancial research questions facing the \curse of dimensionality". This thesis endeavors to utilize some newly developed statistical methods to address the \curse of dimensionality" in nancial research, while providing new perspectives on the economic and nancial implications. For instance, Chapter One of this thesis addresses the \factor zoo enigma" while taking account of high correlations observed between factors. I introduce a newly developed machine learning method to dissect this chaotic factor zoo: the OWL estimator, which is not only e cient in dimension reduction but also robust with correlated variables. Chapter Two extends the econometric theory of the OWL estimator I derived in Chapter One, and mainly concerns the underlying statistical properties of the OWL estimator under less restrictive conditions. Furthermore, I utilize the nodewise LASSO technique to identify and quantify the bias in the OWL estimator and I propose the de-biased OWL estimator before deriving its asymptotic normality property. Chapter Three employs the OWL shrinkage method in the portfolio optimization problems, to exploit contemporaneous relations between stocks. I also develop a exible algorithm which can incorporate bespoke constraints on portfolio weights should investors have any prior information on individual stocks. This thesis covers a broad range of research areas spanning between empirical asset pricing and econometric inferences. It contributes to the literature concerning high-dimensional statistics, with an emphasis on the LASSO-type estimators, while taking account of correlated variables. It also contributes to the empirical asset pricing literature: this thesis sheds light on new perspectives of the \factor zoo enigma", where the importance of factor correlations is highlighted. It also enriches the literature pertaining to portfolio optimization problems. The OWL shrinkage method o ers an extension to the existing LASSO shrinkage method while further exploiting stocks' contemporaneous relations

Essays in High Frequency Trading, Portfolio Selection and Oil Futures Markets

High frequency trading (HFT) requires a detailed analysis of the quote structure of the continuous limit order book in order to correctly de- rive viable arbitrage strategies. Traders can manipulate order books by submitting and retracting ‘spoof’ orders at various levels of the order book by introducing, quote volume at or above (below) the best ask(bid). However, the limit order book data for heavily traded finan- cial instruments presents an almost unique problem to the econome- trician interested in constructing high frequency measures of liquidity impact over and above the inside spread. A single month of data for an individual maturity of an activity traded futures contract, in our example light crude, can easily exceed 10 Billion bytes of data, even when stored using the single precision floating point format. In this thesis we conduct a large scale analysis of the West Texas Inter- mediate (WTI) futures contract across the 120 simultaneously traded maturities for five levels of the order book from 2008 to 2016 sample at the continuous limit. Using this very-large data-set we estimate a new form of realized vector autoregression and derive the impulse re- sponse functions useful in building a HFT strategy. we show that for WTI futures a speed of execution of the order of 100s of milliseconds is needed to fully exploit a false quoting strategy designed to system- atically unbalance the order flow. Furthermore, we demonstrate that viable strategies can be built by spoofing up to three levels above the inside spread. A second part of the thesis involves creating new bootstrap routines to extract meaningful composition data to generate factor pricing mod- els from high frequency data. The key element of this analysis is in understanding the eigendecomposition and subsequent principal com- ponent analysis to extract factors from the data. our bootstrap is new and we provide an analysis of power and consistency in correct- ing bias in the estimation of the eigenstructure and hence evaluating the optimal number of principal components within the data

Information, volatility and price discovery in oil futures markets

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis presents four related empirical essays which investigate the role of information in crude oil futures markets. The first line of investigation examines the impact of futures trading on spot price volatility and finds that the nature of spot price volatility is affected by derivative trading and the improvements in information discovery which such trading brings. Second, the efficiency of futures markets is examined with respect to their ability to provide unbiased estimates of future spot prices. Here it is concluded that while unbiased estimates are generally provided in the long-term, they tend to be largely biased over the short-term. The third area of investigation looks at the relative ability of contemporaneous spot and futures prices to discover information, where it is found that futures generally exhibit price discovery over spot markets but that the relationship can vary considerably over time and in relation to market conditions. In addition, the investigation suggests that previous studies into such relationships have failed to account for all routes through which information passes between spot and futures markets. Finally the thesis probes the question of the relationship within futures markets between volume, volatility and information. The finding is' that futures markets' prices and trading volume exhibit a positive relation and are jointly driven by the rate of information arrival. The results further suggest that the widely held expectation that volume statistics can improve forecasts of future price change does not hold in the case of oil futures. The overall finding of the thesis is that oil futures markets are well-functioning and in general are of benefit to the underlying spot market