[QUOTE]Quantitative tools have been widely adopted in order to extract the massive information from a variety of financial data. Mathematics, statistics and computers algorithms have never been so important to financial practitioners in history. Investment banks develop equilibrium models to evaluate financial instruments; mutual funds applied time series to identify the risks in their portfolio; and hedge funds hope to extract market signals and statistical arbitrage from noisy market data. The rise of quantitative finance in the last decade relies on the development of computer techniques that makes processing large datasets possible. As more data is available at a higher frequency, more researches in quantitative finance have switched to the microstructures of financial market. High frequency data is a typical example of big data that is characterized by the 3V’s: velocity, variety and volume. In addition, the signal to noise ratio in financial time series is usually very small. High frequency datasets are more likely to be exposed to extreme values, jumps and errors than the low frequency ones. Specific data processing techniques and quantitative models are elaborately designed to extract information from financial data efficiently. In this chapter, we present the quantitative data analysis approaches in finance. First, we review the development of quantitative finance in the past decade. Then we discuss the characteristics of high frequency data and the challenges it brings. The quantitative data analysis consists of two basic steps: (i) data cleaning and aggregating; (ii) data modeling. We review the mathematics tools and computing technologies behind the two steps. The valuable information extracted from raw data is represented by a group of statistics. The most widely used statistics in finance are expected return and volatility, which are the fundamentals of modern portfolio theory. We further introduce some simple portfolio optimization strategies as an example of the application of financial data analysis. Big data has already changed financial industry fundamentally; while quantitative tools for addressing massive financial data still have a long way to go. Adoptions of advanced statistics, information theory, machine learning and faster computing algorithm are inevitable in order to predict complicated financial markets. These topics are briefly discussed in the later part of this chapter.[/QUOTE]

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Automated high-frequency trading has grown tremendously in the past 20 years and is responsible for about half of all trading activities at stock exchanges worldwide. Geography is central to the rise of high-frequency trading due to a market design of “continuous trading” that allows traders to engage in arbitrage based upon informational advantages built into the socio-technical assemblages that make up current capital markets. Enormous investments have been made in creating transmission technologies and optimizing computer architectures, all in an effort to shave milliseconds of order travel time (or latency) within and between markets. We show that as a result of the built spatial configuration of capital markets, “public” is no longer synonymous with “equal” information. High-frequency trading increases information inequalities between market participants.

High-frequency trading and the construction of information inequality.pdf
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n the age of automation, trading and market making is about estimating the fair price of automated trading system research and development projects. This requires a new methodology to arrive at such a fair price. A real options framework is a natural choice. In this paper we review a methodology for automated trading system R&D and present a practical real option model for valuing such projects so as to enable rapid strategy cycling.



A Practical Real Options Approach to Valuing High-Frequ... R&D Projects.pdf
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This paper studies correlations between the strategies of high-frequency trading (HFT) firms, which is a manifestation of the extent of competition in which these firms engage when pursuing similar strategies. We use a principal component analysis to show that there are several underlying common strategies and that the competing HFT firms pursuing these strategies generate most HFT activity. We investigate whether competition between HFT firms creates a systematic return factor, but find no supporting evidence for such an influence. However, the short-interval return volatility of most stocks loads negatively on a market-wide measure of correlated HFT strategies. The mitigating impact of HFT competition on stock volatility appears to be driven at least in part by a market-making strategy. We further document a negative relationship between two forms of competition—that between HFT firms and that between trading venues. We investigate a potential driver behind this negative relationship, and show that greater HFT competition within a trading venue helps smaller trading venues become more competitive or viable in terms of posting better prices and narrower spreads.

Correlated High-Frequency Trading.pdf
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In this paper we present a simple closed form stock price formula, which captures empirical regularities of high frequency trading (HFT), based on two factors: (1) exposure to hedge factor; and (2) hedge factor volatility. Thus, the parsimonious formula is not based on fundamental valuation. For applications, we first show that in tandem with a cost of carry model, it allows us to use exposure to and volatility of E-mini contracts to estimate dynamic hedge ratios, and mark-to-market capital gains on contracts. Second, we show that for given exposure to hedge factor, and suitable specification of hedge factor volatility, HFT stock price has a closed form double exponential representation. There, in periods of uncertainty, if volatility is above historic average, a relatively small short selling trade strategy is magnified exponentially, and the stock price plummets when such strategies are phased locked for a sufficient large number of traders. Third, we demonstrate how asymmetric response to news is incorporated in the stock price by and through an endogenous EGARCH type volatility process for past returns; and find that intraday returns have a U-shaped pattern inherited from HFT strategies. Fourth, we show that for any given sub-period, capital gains from trading is bounded from below (crash), i.e. flight to quality, but not from above (bubble), i.e. confidence, when phased locked trade strategies violate prerequisites of van der Corput's Lemma for oscillatory integrals. Fifth, we provide a taxonomy of trading strategies which reveal that high HFT Sharpe ratios, and profitability, rests on exposure to hedge factor, trading costs, volatility thresholds, and algorithm ability to predict volatility induced by bid-ask bounce or otherwise. Thus, extant regulatory proposals to control price dynamics of select stocks, i.e., pause rules such as ''limit up/limit down" bands over 5-minute rolling windows, may mitigate but not stop future market crashes or price bubbles from manifesting in underlying indexes that exhibit HFT stock price dynamics.
Trading Rules Over Fundamentals - A Stock Price Formula...s and Crashes.pdf
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[QUOTE]Recent publications reveal that high frequency trading (HFT) is responsible for 10 to 70 per cent of the order volume in stock and derivatives trading (Gomber et al. 2011; Hendershott and Riordan 2011; Zhang 2010). This observation leads to a controversial debate over positive and negative implications of HFT for the liquidity and efficiency of electronic securities markets and over the costs and benefits of and needs for market regulation. Currently the European Union (EU) is considering the introduction of a financial transaction tax to curtail the harmful effects of HFT strategies. The consideration behind this market policy is based on the assumption that the very short-term oriented HFT trading strategies lead to market frictions. This current discourse shows that the arguing parties do not homogeneously define HFT. Reasons for this are the proponents’ different but intertwined perspectives, which lead to new unanswered questions in numerous subjects of expertise.
High Frequency Trading.pdf
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Re: High Frequency Trading

We define low-latency activity as strategies that respond to market events in the millisecond environment, the hallmark of proprietary trading by high-frequency trading firms. We propose a new measure of low-latency activity that can be constructed from publicly-available NASDAQ data to investigate the impact of high-frequency trading on the market environment. Our measure is highly correlated with NASDAQ-constructed estimates of high-frequency trading, but it can be computed from data that are more widely-available. We use this measure to study how low-latency activity affects market quality both during normal market conditions and during a period of declining prices and heightened economic uncertainty. Our conclusion is that increased low-latency activity improves traditional market quality measures — lowering short-term volatility, decreasing spreads, and increasing displayed depth in the limit order book. Of particular importance is that our findings suggest that increased low-latency activity need not work to the detriment of long-term investors in the current market structure for U.S. equities.
Low-Latency Trading.pdf
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How Does High Frequency Trading Affect Low Frequency Trading?

High frequency trading dominates trading in financial markets. How it affects the low frequency trading, however, is still unclear. Using NASDAQ order book data, we investigate this question by categorizing orders as either high or low frequency, and examining several measures. We find that high frequency trading enhances liquidity by increasing the trade frequency and quantity of low frequency orders. High frequency trading also reduces the waiting time of low frequency limit orders and improves their likelihood of execution. Our results indicate that high frequency trading has a liquidity provision effect and improves the execution quality of low frequency orders.
How Does High Frequency Trading Affect Low Frequency Trading.pdf
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Risk and Return in High-Frequency Trading

We study performance and competition among high-frequency traders (HFTs). We construct measures of latency and find that differences in relative latency account for large differences in HFTs’ trading performance. HFTs that improve their latency rank due to colocation upgrades see improved trading performance. The stronger performance associated with speed comes through both the short-lived information channel and the risk management channel, and speed is useful for a variety of strategies including market making and cross-market arbitrage. We explore implications of competition on relative latency and find support for various theoretical predictions.
Risk and Return in High-Frequency Trading.pdf
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Middlemen in Limit Order Markets

A limit order market enables an early seller to trade with a late buyer by leaving a price quote. Information arrival in the interim period creates adverse selection risk for the seller and therefore hampers trade. Entry of high-frequency traders (HFTs) might restore trade as their machines can refresh quotes quickly on (hard) information. Empirically, HFT entry reduced adverse selection by 23% and increased trade by 17%. Model calibration shows that one percentage point more of the gains from trade were realized. Finally, we show that a well-designed double auction raises this to ten percentage points.
Middlemen in Limit Order Markets.pdf
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