Pairs trading with a mean-reverting jump–diffusion model on high-frequency data

This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a three-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads’ mean-reversion speed and jump behaviour. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61% p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk–return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.     

A test of the Investor's Daily stock ranking system

This paper examines the profitability of trading strategies derived from stock rankings published in Investor's Business Daily. The best system provides market-adjusted abnormal monthly returns of 1.81% from buying S&P 500 stocks, and a 3.18% abnormal return on an arbitrage portfolio. Stocks selected for trading have above average volatility, but a portion of abnormal return may be a reward for identifying stocks with short-run sustainable price momentum. Results seem indicative of market inefficiency, but the phenomena may be temporary since abnormal returns are lower during the second half of the data set.     

Price reversal,transaction costs,and arbitrage profits in the real estate securities market

This paper studies the return reversals of exchange traded real estate securities using an arbitrage portfolio approach. Using the approach, we find that there exist significant return reversals in such securities. These return reversals could be exploited by arbitrage traders if trading costs can be ignored. However, the arbitrage profits disappear after deducting trading costs and taking into account the implicit cost of bid-ask spread. Thus, the real estate securities market is efficient at weekly intervals in the sense that one could not exploit the price reversals via some simple trading rules.     

How does electronic trading affect efficiency of stock market and conditional volatility? Evidence from Toronto Stock Exchange

The present paper investigates informational efficiency and changes in conditional volatility of the TSX before and after the implementation of an automated trading system on April 23, 1997. Using a battery of unit root, stationarity, as well as linear tests, we find that the introduction of electronic trading led to an increase in linearity dependence in TSX daily returns. In addition, when we examined the nonlinearity dependences using powerful econometric tests, we find that electronic trading has increased nonlinear dependencies in return series, which is the main cause of rejecting the Random Walk Hypothesis (RWH). Our results suggest that the automated trading system has negatively affected informational efficiency of the TSX. We also find evidence of long memory following automation which suggests that the introduction of electronic trading has increased the level of persistence of information and trading shocks.     

Intraday Return Volatility Process: Evidence from NASDAQ Stocks

This paper presents a comprehensive analysis of the distributional and time-series properties of intraday returns. The purpose is to determine whether a GARCH model that allows for time varying variance in a process can adequately represent intraday return volatility. Our primary data set consists of 5-minute returns, trading volumes, and bid-ask spreads during the period January 1, 1999 through March 31, 1999, for a subset of thirty stocks from the NASDAQ 100 Index. Our results indicate that the GARCH(1,1) model best describes the volatility of intraday returns. Current volatility can be explained by past volatility that tends to persist over time. These results are consistent with those of Akgiray (1989) who estimates volatility using the various ARCH and GARCH specifications and finds the GARCH(1,1) model performs the best. We add volume as an additional explanatory variable in the GARCH model to examine if volume can capture the GARCH effects. Consistent with results of Najand and Yung (1991) and Foster (1995) and contrary to those of Lamoureux and Lastrapes (1990), our results show that the persistence in volatility remains in intraday return series even after volume is included in the model as an explanatory variable. We then substitute bid-ask spread for volume in the conditional volatility equation to examine if the latter can capture the GARCH effects. The results show that the GARCH effects remain strongly significant for many of the securities after the introduction of bid-ask spread. Consistent with results of Antoniou, Homes and Priestley (1998), intraday returns also exhibit significant asymmetric responses of volatility to flow of information into the market.     

Stock returns,trading volume,and volatility: The case of African stock markets

The presence of the African Stock Markets (ASMs) in the global frontier markets indices confirms their global portfolio diversification role. This study investigates the asymmetric and intertemporal causality among the stock returns, trading volume, and volatility of eight ASMs. Results based on the linear model reveal that return generally Granger cause trading volume. However, evidence from the quantile regression shows that lagged trading volume has a negative causal effect on returns at low quantiles and positive causal effects at high quantiles. This evidence is consistent with volume-return equilibrium models, disposition and overconfidence models, and information asymmetry models. The positive causal effects of volatility on volume support the dispersion of beliefs model. In contrast, intertemporal evidence of contemporaneous and lagged causal relationships from trading volume to volatility supports the mixture of distribution hypothesis, sequential information acquisition hypothesis, and dynamic efficient market hypothesis. Volume-return and return-volume causality dynamics are quantile-specific and therefore driven by market conditions. However, the volume-volatility causality is dependent on volatility regimes. The linear model results confirm how model misspecification can distort and even reverse empirical evidence relative to nonlinear models.     

中国信用规模与经济增长关系的实证研究——基于1986～2004年的协整分析

本文以中国经济改革和金融发展为背景,运用协整检验和误差纠正模型对中国信用规模与经济增长的长期稳定关系进行研究.协整分析结果表明,GDP与信用总规模之间存在协整关系,信用总规模对经济增长的拉动作用明显;GDP与金融信用、企业信用和政府信用规模之间同样存在协整关系,GDP与金融信用和企业信用规模有较强的正向关系,但是GDP与政府信用规模之间存在负向关系.此外,误差纠正模型结果表明,校正作用较为明显.     

Variations in Trading Volume,Return Volatility,and Trading Costs: Evidence on Recent Price Formation Models

Patterns in stock market trading volume, trading costs, and return volatility are examined using New York Stock Exchange data from 1988. Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half-hour of the day. This evidence is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatility are high. Interday test results show that, for actively traded firms, trading volume is low and adverse selection costs are high on Monday, which is consistent with the predictions of the Foster and Viswanathan (1990) model.     

Examining the Equilibrium Relationship Between the Shanghai 50 Stock Index Futures and the Shanghai 50 ETF Options Markets

Based on the put-call-futures parity model, this article studies the equilibrium relationship between the Shanghai 50 stock index futures and the Shanghai 50 Exchange-Traded Fund (ETF) options markets by analyzing the arbitrage opportunities and profits between these two derivative markets. This article reveals that the cost spread, option volatility, days from the expiration date, moneyness of options, trading strategy, and policy factors all have a great impact on the arbitrage profits and opportunities. In addition, significant arbitrage profits and opportunities indicate violations of put-call-futures parity. Although no equilibrium relationship exists between the Shanghai 50 stock index futures and the Shanghai 50 ETF options markets, efficiency in these markets has gradually improved.     

Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns

Recent empirical evidence suggests that the interdaily volatility clustering for most speculative returns are best characterized by a slowly mean-reverting fractionally integrated process. Meanwhile, much shorter lived volatility dynamics are typically observed with high frequency intradaily returns. The present article demonstrates, that by interpreting the volatility as a mixture of numerous heterogeneous short-run information arrivals, the observed volatility process may exhibit long-run dependence. As such, the long-memory characteristics constitute an intrinsic feature of the return generating process, rather than the manifestation of occasional structural shifts. These ideas are confirmed by our analysis of a one-year time series of five-minute Deutschemark-U.S. Dollar exchange rates.     

Does Bitcoin behave as a currency?: A standard monetary model approach

We derive the Bitcoin exchange rate dynamics by solving the exchange rate equation of the standard flexible-price monetary model to investigate any characteristics of Bitcoin like a currency. The dynamics is driven by an asymmetric mean-reverting fundamental shock which can be attributed to a money demand shock. A crash occurs when the exchange rate with a weakened mean-reverting force breaches a lower boundary where a smooth-pasting condition is imposed. The empirical results show the exchange rate dynamics can be calibrated according to the model, in which the mean reversion of the dynamics is positively co-integrated with the Bitcoin transaction volume indicating demand for Bitcoin; and with the risk reversals of the commodity currencies (Australian dollar and Canadian dollar) in currency option markets. The analysis shows that the Bitcoin exchange rate shares some characteristics of commodity currencies with crash risk. This suggests that Bitcoin behaves as a currency between fiat money and a crypto-commodity used for trading and investment purposes.     

The Effect of Option Listing on Bid-Ask Spreads,Price Volatility,and Trading Activity of the Underlying OTC Stocks

This paper examines the changes in spreads, price volatility, and trading activity surrounding option listing for a sample of 144 OTC stocks. For this sample, both price volatility and volume increase, but the evidence on spreads is mixed. The increase in price volatility is attributed primarily to an increase in residual return variances. Furthermore, price volatility increases even after controlling for volume, insider trading, and spreads. Although these variables do not fully explain the causes for the increase in price volatility after option listing, the results suggest that liquidity trading or volume has a stronger effect on price volatility than insider trading. This study also finds that both the number of trades and institutional holdings show substantial increases, which are supportive of the notion that listing of options on OTC stocks attracts more attention.     

Circuit Breakers,Trading Collars,and Volatility Transmission Across Markets: Evidence from NYSE Rule 80A

The NYSE's Rule 80A attempted to delink the futures and equity markets by limiting index arbitrage trades in the same direction as the last trade to reduce stock market volatility. Rule 80A leads to a small but statistically significant decline in intraday U.S. equity market volatility. In addition, the results are asymmetric: volatility is dampened more in a rising market than in a declining one. These results suggest that, to a limited extent, rule restrictions on trading can sufficiently delink the futures and equity markets enough to reduce the transmission of volatility.     

Intra–day Behavior of Treasury Sector Index Option Implied Volatilities around Macroeconomic Announcements

If option implied volatility is an unbiased, efficient forecast of future return volatility in the underlying asset, then we should be able to predict its path around macroeconomic announcements from responses in cash markets. Regressions show that volatilities rise the afternoon before announcements that move cash markets, and that post–announcement volatilities return to normal as rapidly as cash prices do. Although implied volatilities are predictable, the Treasury options market is efficient since informed traders do not earn arbitrage profits once we account for trading costs.     

A pairs trading strategy based on linear state space models and the Kalman filter

Among many strategies for financial trading, pairs trading has played an important role in practical and academic frameworks. Loosely speaking, it involves a statistical arbitrage tool for identifying and exploiting the inefficiencies of two long-term, related financial assets. When a significant deviation from this equilibrium is observed, a profit might result. In this paper, we propose a pairs trading strategy entirely based on linear state space models designed for modelling the spread formed with a pair of assets. Once an adequate state space model for the spread is estimated, we use the Kalman filter to calculate conditional probabilities that the spread will return to its long-term mean. The strategy is activated upon large values of these conditional probabilities: the spread is bought or sold accordingly. Two applications with real data from the US and Brazilian markets are offered, and even though they probably rely on limited evidence, they already indicate that a very basic portfolio consisting of a sole spread outperforms some of the main market benchmarks.     

The price discovery of day trading activities in futures market

Access to information is necessary for market transparency. However, contrary to trading volume and open interest, information related to day trading activities is rarely available. By incorporating unexplored day trading volume in the literature, this paper demonstrates that both the expected open interest and expected day trading volume are consistently and positively correlated with returns, but that one-lagged day trading volume is negatively correlated with futures returns. Meanwhile, both expected and unexpected day trading volume are negatively correlated with volatility, suggesting that arbitrage activities related to unexpected day trading volume may accelerate the movement of futures prices to a new equilibrium. Moreover, open interest provides liquidity but increases volatility. Finally, we strongly suggest that day trading transaction information be released by futures exchanges to achieve greater transparency.     

Noise trading in small markets: Evidence from Amman Stock Exchange (ASE)

This study aims to analyze the behavior of traders in Amman Stock Exchange (ASE):-firstly at the market level by analyzing the market return volatility, defining the time frame of this volatility, and classifying it as transitory volatility or a permanent volatility, Daily closing of Amman free float market index will be used to indicate the market return during the period from 1/1/1992 to 31/12/2015 where 5899 observations were obtained. Secondly at the firms level by selecting a sample of trading companies and interpreting the results through analyzing some important features of the companies, such as share price and ownership structure, Daily closing of share price of the selected companies will be used to indicate the return during the period from 1/1/2015 to 31/12/2015 where 240 observations were obtained for each company during this period.To achieve the goals of this study, the Variance ratio test, GARCH test, and CGARCH test will be used. The study highlighted an important result that the common culture of traders on ASE was Noise Trading; the significance of this finding was statistically proven at the confidence level of 1%.This study recommends the competent authorities to enact a slew of strict measures: the implementation of Capital Gains Tax in a bid to slash frequent selloffs and purchasing of noise traders and increasing the commission of brokers in return for completing selloffs and purchasing deals. The study also affirmed the necessity of intervening periodically to raise awareness of the negative impact of speculation including the instability, increasing the firm’s cost of capital and the damage to traders’ confidence in the stock markets.     

Disagreement and equilibrium option trading volume

Using a complete market equilibrium model, we present results concerning the effect disagreement has on equilibrium option trading volume and positioning. We find that if agents agree on volatility, total option volume is independent of wealth distribution and average optimism. We also find option volume increasing in drift disagreement and decreasing in risk aversion and volatility. Pessimists are shown to write most options. With volatility disagreement, the results are less clear; however, we show agents with high volatility beliefs write deep out of the money options and buy close to the money options. Numerical comparative statics are also performed. This revised version was published online in June 2006 with corrections to the Cover Date.     

The perception of time,risk and return during periods of speculation

Abstract

What return should you expect when you take on a given amount of risk? How should that return depend upon other people's behaviour? What principles can you use to answer these questions? In this paper, I approach these topics by exploring the consequences of two simple hypotheses about risk.

The first is a common-sense invariance principle: assets with the same perceived risk must have the same expected return. It leads directly to the well known Sharpe ratio and the classic risk-return relationships of arbitrage pricing theory and the capital asset pricing model.

The second hypothesis concerns the perception of time. I conjecture that in times of speculative excitement, short-term investors may instinctively imagine stock prices to be evolving in a time measure different from that of calendar time. They may perceive and experience the risk and return of a stock in intrinsic time, a dimensionless time scale that counts the number of trading opportunities that occur, but pays no attention to the calendar time that passes between them.

Applying the first hypothesis in the intrinsic time measure suggested by the second, I derive an alternative set of relationships between risk and return. Its most noteworthy feature is that, in the short-term, a stock's trading frequency affects its expected return. I show that short-term stock speculators will expect returns proportional to the temperature of a stock, where temperature is defined as the product of the stock's traditional volatility and the square root of its trading frequency. Furthermore, I derive a modified version of the capital asset pricing model in which a stock's excess return relative to the market is proportional to its traditional beta multiplied by the square root of its trading frequency.

I also present a model for the joint interaction of long-term calendar-time investors and short-term intrinsic-time speculators that leads to market bubbles characterized by stock prices that grow super-exponentially with time.

Finally, I show that the same short-term approach to options speculation can lead to an implied volatility skew.

I hope that this model will have some relevance to the behaviour of investors expecting inordinate returns in highly speculative markets.     

Noise, equity prices, and hedging: A new approach

The existence of noise trading in equity markets has possible economic implications for arbitrage, and asset pricing. In terms of pricing, noise trading can lead to excess volatility which has been shown to influence the value of options and futures. Furthermore, option research shows that modeling volatility leads to improved hedging performance. To this end, we derive a general hedging model for equity index futures in the presence of noise trading. Our analysis shows how the level and dynamics of noise trading should influence a hedger's behavior. Finally, we empirically test our model using the NASDAQ-100 index futures and FTSE 100 index futures over the period of January 1998 to May 2003.