Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation

Linear and nonlinear Granger causality tests are used to examine the dynamic relation between daily Dow Jones stock returns and percentage changes in New York Stock Exchange trading volume. We find evidence of significant bidirectional nonlinear causality between returns and volume. We also examine whether the nonlinear causality from volume to returns can be explained by volume serving as a proxy for information flow in the stochastic process generating stock return variance as suggested by Clark's (1973) latent common-factor model. After controlling for volatility persistence in returns, we continue to find evidence of nonlinear causality from volume to returns.     

Invisible Parameters in Option Prices

This paper characterizes contingent claim formulas that are independent of parameters governing the probability distribution of asset returns. While these parameters may affect stock, bond, and option values, they are “invisible” because they do not appear in the option formulas. For example, the Black-Scholes ( 1973 ) formula is independent of the mean of the stock return. This paper presents a new formula based on the log-negative-binomial distribution. In analogy with Cox, Ross, and Rubinstein's ( 1979 ) log-binomial formula, the log-negative-binomial option price does not depend on the jump probability. This paper also presents a new formula based on the log-gamma distribution. In this formula, the option price does not depend on the scale of the stock return, but does depend on the mean of the stock return. This paper extends the log-gamma formula to continuous time by defining a gamma process. The gamma process is a jump process with independent increments that generalizes the Wiener process. Unlike the Poisson process, the gamma process can instantaneously jump to a continuum of values. Hence, it is fundamentally “unhedgeable.” If the gamma process jumps upward, then stock returns are positively skewed, and if the gamma process jumps downward, then stock returns are negatively skewed. The gamma process has one more parameter than a Wiener process; this parameter controls the jump intensity and skewness of the process. The skewness of the log-gamma process generates strike biases in options. In contrast to the results of diffusion models, these biases increase for short maturity options. Thus, the log-gamma model produces a parsimonious option-pricing formula that is consistent with empirical biases in the Black-Scholes formula.     

Jump robust two time scale covariance estimation and realized volatility budgets

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct the ex-post portfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009.     

Stock market trading activity and returns around milestones

We study the relation between daily stock market trading activity and the Dow Jones Industrial Average's (DJIA) movement around millenary milestones—numbers that end in three zeros. We find aggregate turnover to be 5% lower when the DJIA level is less than 1% away from the nearest milestone. The effect emerges as the DJIA approaches a milestone from below, and is stronger for first-time milestones compared to subsequent passages. The aggregate price impact is large, such that daily stock returns show a negative abnormal performance of − 10 basis points. Our findings suggest that millenary milestones of the DJIA play a role in some investors' decision making.     

Is All That Talk Just Noise? The Information Content of Internet Stock Message Boards

Financial press reports claim that Internet stock message boards can move markets. We study the effect of more than 1.5 million messages posted on Yahoo! Finance and Raging Bull about the 45 companies in the Dow Jones Industrial Average and the Dow Jones Internet Index. Bullishness is measured using computational linguistics methods. Wall Street Journal news stories are used as controls. We find that stock messages help predict market volatility. Their effect on stock returns is statistically significant but economically small. Consistent with Harris and Raviv (1993) , disagreement among the posted messages is associated with increased trading volume.     

What Does the Corporate Bond Market Know?

Do related markets reflect new information simultaneously? For high‐yield bonds, a large abnormal price decline in a corporation's most liquid bond over a month is followed by an average abnormal stock price decline of ?1.42%. This effect is larger for stocks that have increased in value and for volatile stocks. It is also larger for bonds with high coupons and shorter maturities. These results support the view that high‐yield corporate bonds have an informational edge when news is negative and stock returns are noisy, and add to the growing literature on the substantial lags in price discovery between related markets.     

What Is the Expected Return on a Stock?

We derive a formula for the expected return on a stock in terms of the risk‐neutral variance of the market and the stock's excess risk‐neutral variance relative to that of the average stock. These quantities can be computed from index and stock option prices; the formula has no free parameters. The theory performs well empirically both in and out of sample. Our results suggest that there is considerably more variation in expected returns, over time and across stocks, than has previously been acknowledged.     

World War II events and the Dow Jones industrial index

This paper investigates which events of World War II (WWII) the US investors (at that time) considered as turning points (structural breaks) of the war. The empirical study employs daily Dow Jones industrial average stock index and volatility from January 1939 to December 1945 and applies structural shift oriented test to determine endogenously the structural breaks during the WWII period. Results show that the majority of the wartime events (on and off the battlefield) labelled important by historians did result in structural breaks in both price movement and stock returns volatility (risk). These results have major implications for investors of the present and future.     

The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

Identifying common dynamic features in stock returns

This paper proposes volatility and spectral based methods for the cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared returns, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the ‘blue-chip’ stocks used to compute the Dow Jones Industrial Average (DJIA) index.     

FORECASTING STOCK INDEX VOLATILITY: COMPARING IMPLIED VOLATILITY AND THE INTRADAY HIGH–LOW PRICE RANGE

The intraday high–low price range offers volatility forecasts similarly efficient to high‐quality implied volatility indexes published by the Chicago Board Options Exchange (CBOE) for four stock market indexes: S&P 500, S&P 100, NASDAQ 100, and Dow Jones Industrials. Examination of in‐sample and out‐of‐sample volatility forecasts reveals that neither implied volatility nor intraday high–low range volatility consistently outperforms the other.     

Identifying multiple outliers in heavy-tailed distributions with an application to market crashes

Heavy-tailed distributions, such as the distribution of stock returns, are prone to generate large values. This renders difficult the detection of outliers. We propose a new outward testing procedure to identify multiple outliers in these distributions. A major virtue of the test is its simplicity. The performance of the test is investigated in several simulation studies. As a substantive empirical contribution we apply the test to Dow Jones Industrial Average return data and find that the Black Monday market crash was not a structurally unusual event.     

The Effect of Volatility Changes on the Level of Stock Prices and Subsequent Expected Returns

This paper estimates volatility changes in daily returns to the Dow Jones Industrial Average over the sample period 1897 through 1988. This allows a direct investigation of the reaction of the level of stock prices and subsequent expected returns to these estimated changes in volatility. We provide empirical evidence consistent with relatively large and systematic revisions in stock prices and subsequent expected returns to volatility changes. However, there appears to be an asymmetry in the market's reaction to volatility increases as opposed to volatility decreases. A majority of our volatility changes cannot be associated with the release of significant economic information.     

The multivariate Variance Gamma model: basket option pricing and calibration

In this paper, we propose a methodology for pricing basket options in the multivariate Variance Gamma model introduced in Luciano and Schoutens [Quant. Finance 6(5), 385–402]. The stock prices composing the basket are modelled by time-changed geometric Brownian motions with a common Gamma subordinator. Using the additivity property of comonotonic stop-loss premiums together with Gauss-Laguerre polynomials, we express the basket option price as a linear combination of Black & Scholes prices. Furthermore, our new basket option pricing formula enables us to calibrate the multivariate VG model in a fast way. As an illustration, we show that even in the constrained situation where the pairwise correlations between the Brownian motions are assumed to be equal, the multivariate VG model can closely match the observed Dow Jones index options.     

Striking oil: Another puzzle?

Changes in oil prices predict stock market returns worldwide. We find significant predictability in both developed and emerging markets. These results cannot be explained by time-varying risk premia as oil price changes also significantly predict negative excess returns. Investors seem to underreact to information in the price of oil. A rise in oil prices drastically lowers future stock returns. Consistent with the hypothesis of a delayed reaction by investors, the relation between monthly stock returns and lagged monthly oil price changes strengthens once we introduce lags of several trading days between monthly stock returns and lagged monthly oil price changes.     

Modelling changes in the unconditional variance of long stock return series

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long daily return series. For this purpose we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2012, 2013). The latter component is modelled such that the unconditional time-varying component evolves slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to 22,986 daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the apparent long memory property in volatility may be interpreted as changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecasting accuracy of the new model over the GJR-GARCH model at all horizons for eight subsets of the long return series.     

Shock around the clock—on the causal relations between international stock markets,the strength of causality and the intensity of shock transmission: an econometric analysis

This paper investigates empirically the interrelationships between the daily stock market returns of the Nikkei 225, DAX and Dow Jones Industrial index. In contrast to former work this paper uses the succession of the markets in time to form different econometric models. In this way it is possible to detect causality not only from the USA to foreign countries but in some cases vice versa. The observation period is October 1985 to October 1997. Analysis of the structural properties leads to the examination of four separated periods. Results for Hosoya’s measure of the strength of causality and impulse response analysis facilitate a dynamic analysis of the causal structure. Increasing influence from NYSE to foreign markets can be shown, whereas influence of the foreign markets on the Dow Jones is decreasing. Copyright © 1999 John Wiley & Sons, Ltd.     

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.