ON THE ROBUSTNESS OF RANGE‐BASED VOLATILITY ESTIMATORS

We empirically examine Parkinson's range‐based volatility estimate in the federal funds market, which is unique because institutional regulations create a predictable pattern in interday volatility. We find that range‐based volatility estimates and standard deviations produce the expected volatility pattern. We also find that at trading pressure points where microstructure noise should be greatest, range‐based estimates are less than the standard deviations. Thus, we support the argument that range‐based volatility estimates remove the upward bias created by microstructure noise. We find that the Parkinson method is the most efficient range‐based volatility measure among a set of alternates in this market.     

The leverage effect puzzle: Disentangling sources of bias at high frequency

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.     

Automation, speed, and stock market quality: The NYSE's Hybrid

Automation and trading speed are increasingly important aspects of competition among financial markets. Yet we know little about how changing a market's automation and speed affects the cost of immediacy and price discovery, two key dimensions of market quality. At the end of 2006 the New York Stock Exchange introduced its Hybrid Market, increasing automation and reducing the execution time for market orders from 10 seconds to less than one second. We find that the change raises the cost of immediacy (bid-ask spreads) because of increased adverse selection and reduces the noise in prices, making prices more efficient.     

Finite sample accuracy and choice of sampling frequency in integrated volatility estimation

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, Fourier, and wavelet estimation, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. Ornstein–Uhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using models with bid-ask bounce and price discreteness, in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bid-ask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias. A brief empirical illustration with high-frequency GE data is also included.     

Testing weak form efficiency on the Toronto Stock Exchange

In order to test for weak form efficiency in the market a vast pool of individual stocks must be analyzed rather than a stock market index. In this paper, a model-based bootstrap is used to generate a series of simulated trials and a modified chart pattern recognition algorithm is applied to all stocks listed on the Toronto Stock Exchange (TSX). The number of patterns detected in the original price series is compared with the number of patterns found in the simulated series. By simulating the price path specific time dependencies present in real data are eliminated, making price changes purely random. Patterns, if consistently identified, carry information which adds value to the investment process, however, this informativeness does not guarantee profitability. Conclusions are drawn on the relative efficiency of some sectors of the economy. Although the null hypothesis of weak form efficiency on the TSX cannot be rejected, some sectors of the Canadian economy appear to be less efficient than others. In addition, pattern frequencies appear to be negatively dependent on the two moments of return distributions, variance and kurtosis.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

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.     

Keep on smiling? The pricing of Quanto options when all covariances are stochastic

The paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.     

International transmission of information: evidence from the Euroyen and Eurodollar futures markets

This paper examines the information transmission between Japan and the US by using the Tokyo Euroyen and Chicago Eurodollar futures. These two interest rate futures markets provide a better understanding of international information transmission than stock markets, which have been shown to exhibit nonsynchronous trading and market segmentation. The results show that traders in Tokyo (Chicago) use information that is revealed overnight in Chicago (Tokyo). The bivariate EGARCH-t model provides no evidence of volatility spillovers in either direction, suggesting that the opening price rapidly reflects foreign information. The overall results support the hypothesis that the domestic market efficiently adjusts to foreign news. The results are also broadly consistent with the covered interest arbitrage effects.     

Portfolio analysis of intraday covariance matrix in the Greek equity market

The intraday nonparametric estimation of the variance–covariance matrix adds to the literature in portfolio analysis of the Greek equity market. This paper examines the economic value of various realized volatility and covariance estimators under the strategy of volatility timing. I use three types of portfolios: Global Minimum Variance, Capital Market Line and Capital Market Line with only positive weights. The estimators of volatilities and covariances use 5-min high-frequency intraday data. The dataset concerns the FTSE/ATHEX Large Cap index, FTSE/ATHEX Mid Cap index, and the FTSE/ATHEX Small Cap index of the Greek equity market (Athens Stock Exchange). As far as I know, this is the first work of its kind for the Greek equity market. Results concern not only the comparison of various estimators but also the comparison of different types of portfolios, in the strategy of volatility timing. The economic value of the contemporary non-parametric realized volatility estimators is more significant than this when the covariance is estimated by the daily squared returns. Moreover, the economic value (in b.p.s) of each estimator changes with the volatility timing.     

Market risk model selection and medium-term risk with limited data: Application to ocean tanker freight markets

The estimation of medium-term market risk dictated by limited data availability, is a challenging issue of concern amongst academics and practitioners. This paper addresses the issue by exploiting the concepts of volatility and quantile scaling in order to determine the best method for extrapolating medium-term risk forecasts from high frequency data. Additionally, market risk model selection is investigated for a new dataset on ocean tanker freight rates, which refer to the income of the capital good — tanker vessels. Certain idiosyncrasies inherent in the very competitive shipping freight rate markets, such as excessive volatility, cyclicality of returns and the medium-term investment horizons – found in few other markets – make these issues challenging. Findings indicate that medium-term risk exposures can be estimated accurately by using an empirical scaling law which outperforms the conventional scaling laws of the square and tail index root of time. Regarding the market risk model selection for short-term investment horizons, findings contradict most studies on conventional financial assets: interestingly, freight rate market risk quantification favors simpler specifications, such as the GARCH and the historical simulation models.     

Testing for long-term memory in yen/dollar exchange rate

This paper examines evidence of long-term memory in the yen/dollar price change as well as in the daily estimate of volatility of the exchange rate series. The methodology used is due to Lo (1989) which is robust to the presence of heteroscedasticity and is applied to a ten year data set. The result shows no evidence of long-term memory in the price change series indicating efficient pricing by the market participants. The volatility series, however, shows evidence of long-term memory which may have implications for traders dealing with long lived assets.     

Determinants of bid and ask quotes and implications for the cost of trading

Financial transaction costs are time varying. This paper proposes a model that relates transaction cost to characteristics of order flow. We obtain qualitatively consistent model results for different stocks and across different time periods. We find that an unusual excess of buyers (sellers) relative to sellers (buyers) tends to increase the ask (bid) price. Hence, the ask and bid components of spread change asymmetrically about the efficient price. For a fixed order imbalance surprise these effects are muted when unanticipated total volume is high. Unexpected high volatility in the transaction price process tends to widen the spread symmetrically about the efficient price. Our findings are consistent with predications from market microstructure theory that the cost of market making should depend on both the risk of trading with better-informed traders and inventory risk. We also find that order flow surprises have a significant impact on the efficient price and can also explain a substantial amount of persistence in the volatility of the efficient price. This dependence does not violate the efficient market hypothesis since the surprises, by definition, are not predictable.     

ARE PRICE LIMITS EFFECTIVE? EVIDENCE FROM THE ISTANBUL STOCK EXCHANGE

There is considerable discussion about controlling volatility by imposing price limits on asset prices. We examine the effects of price limits on a stock market by testing the volatility spillover, delayed price discovery, and trading interference hypotheses in a leading emerging market, the Istanbul Stock Exchange, which has a unique market microstructure as related to price limits. Our results support the volatility spillover, delayed price discovery, and trading interference hypotheses. We also show price locks at limits provide significantly stronger evidence regarding the effects of price limits than limit moves only. Finally, price limits have a significant effect on the stock market, casting doubt on their effectiveness.     

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.     

Stock market volatility and equity returns: Evidence from a two-state Markov-switching model with regressors

This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra- and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the ‘rebound’ model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than short-horizon investors.     

Evidence of an asymmetry in the relationship between volatility and autocorrelation

This paper focuses on the general determinants of autocorrelation and the relationship between autocorrelation and volatility in particular. Using UK stock market index and individual stock price data, a multivariate generalized autoregressive conditional heteroskedasticity (M-GARCH) model is used to generate estimates of conditional autocorrelation. The covariance equation of this model is modified to include the potential determinants of autocorrelation including volatility, which is proxied using the time series of filtered probabilities of a Markov regime switching model. Consistent with the previous literature, this paper documents a negative relationship between volatility and autocorrelation. The results suggest that an asymmetry exists in this relationship which is attributed to the constraints placed on short selling.     

Model-free hedge ratios and scale-invariant models

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.     

Transaction Costs and Price Volatility: New Evidence from the Tokyo Stock Exchange

We investigate the volatility impacts of the full commission deregulation in Japan in October 1999, and find that the deregulation overall tends to significantly increase price volatility in the Japanese equity market, using alternative model specifications and control variables. This finding contrasts with previous evidence that implies a positive relation between transaction costs and price volatility, while consistent from the converse with the hypothesis proposed by Stiglitz (1989) and Summers and Summers (1989). Our results suggest that imposing higher transaction costs might still be a feasible policy tool for stabilizing the market by curbing short-term noise trading.

The cost of capital- the practitioners view

The application of a SWARCH model to stock market returns allows one to endogenously determine the regime dependence of the stock market volatility. Comparison of the results from a sample of daily data from five major stock markets shows that the majority of the markets switch regimes simultaneously. This fact is used to investigate the relation between market volatility and the behaviour of the variance—;covariance matrix. It is found that the international variance—;covariance matrix is not stable and that changes in the matrix are dependent on the volatility regime. A high level of variance causes an increase in the average correlation coefficient. The co-movement of the markets is further described by a steady increase in the covariance over the whole sample period. It can be shown that both the time component and the regime dependence of the average correlation have separate and significant explanatory power.