Realized volatility forecasting and market microstructure noise

We extend the analytical results for reduced form realized volatility based forecasting in ABM (2004) to allow for market microstructure frictions in the observed high-frequency returns. Our results build on the eigenfunction representation of the general stochastic volatility class of models developed byMeddahi (2001). In addition to traditional realized volatility measures and the role of the underlying sampling frequencies, we also explore the forecasting performance of several alternative volatility measures designed to mitigate the impact of the microstructure noise. Our analysis is facilitated by a simple unified quadratic form representation for all these estimators. Our results suggest that the detrimental impact of the noise on forecast accuracy can be substantial. Moreover, the linear forecasts based on a simple-to-implement ‘average’ (or ‘subsampled’) estimator obtained by averaging standard sparsely sampled realized volatility measures generally perform on par with the best alternative robust measures.     

Jumps and betas: A new framework for disentangling and estimating systematic risks

We provide a new theoretical framework for disentangling and estimating the sensitivity towards systematic diffusive and jump risks in the context of factor models. Our estimates of the sensitivities towards systematic risks, or betas, are based on the notion of increasingly finer sampled returns over fixed time intervals. We show consistency and derive the asymptotic distributions of our estimators. In an empirical application of the new procedures involving high-frequency data for forty individual stocks, we find that the estimated monthly diffusive and jump betas with respect to an aggregate market portfolio differ substantially for some of the stocks in the sample.     

The bull and bear market model of Huang and Day: Some extensions and new results

We develop a financial market model with interacting chartists and fundamentalists that embeds the famous bull and bear market model of Huang and Day as a special case. Their model is given by a one-dimensional continuous piecewise-linear map. Our model, on the other hand, is more flexible and is represented by a one-dimensional discontinuous piecewise-linear map. Nevertheless, we are able to provide a more or less complete analytical treatment of the model dynamics by characterizing its possible outcomes in parameter space. In addition, we show that quite different scenarios can trigger real-world phenomena such as bull and bear market dynamics and excess volatility.     

Semi-parametric estimation of American option prices

We introduce a novel semi-parametric estimator of American option prices in discrete time. The specification is based on a parameterized stochastic discount factor and is nonparametric w.r.t. the historical dynamics of the Markovian state variables. The historical transition density estimator minimizes a distance built on the Kullback–Leibler divergence from a kernel transition density, subject to the no-arbitrage restrictions for a non-defaultable bond, the underlying asset and some American option prices. We use dynamic programming to make explicit the nonlinear restrictions on the Euclidean and functional parameters coming from option data. We study asymptotic and finite sample properties of the estimators.     

Hermite polynomial based expansion of European option prices

We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no requirements for affine dynamics or explicit characteristic functions. Moreover, convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices, in contrast with small-time asymptotic expansions in the literature. With closed-form expansions, we explicitly translate model features into option prices, such as mean-reverting drift and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach and its advantage over alternative expansion methods.     

Firms’ fundamentals,macroeconomic variables and quarterly stock prices in the US

This paper modeled the effects of firms’ fundamentals such as total assets and long-term debt and of macroeconomic variables such as unemployment and interest rates on quarterly stock prices of over 3000 US firms in the period 2000–07. The merged CRSP/Compustat database was augmented by macroeconomic variables and comprehensive dynamic models were estimated by maximum likelihood taking into account heterogeneity across firms. Likelihood ratio statistics were developed for sequentially testing hypotheses regarding the adequacy of macroeconomic variables in the models. The main findings were that the estimated coefficients of lagged stock prices in simple dynamic random effects models were in the interval 0.90–0.95. Second, comprehensive dynamic models for stock prices showed that the firms’ earnings per share, total assets, long-term debt, dividends per share, and unemployment and interest rates were significant predictors; there were significant interactions between firms’ long-term debt and interest rates. Finally, implications of the results for corporate policies are discussed.     

An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.     

Risk,jumps, and diversification

We test for price discontinuities, or jumps, in a panel of high-frequency intraday stock returns and an equiweighted index constructed from the same stocks. Using a new test for common jumps that explicitly utilizes the cross-covariance structure in the returns to identify non-diversifiable jumps, we find strong evidence for many modest-sized, yet highly significant, cojumps that simply pass through standard jump detection statistics when applied on a stock-by-stock basis. Our results are further corroborated by a striking within-day pattern in the significant cojumps, with a sharp peak at the time of regularly scheduled macroeconomic news announcements.     

Forecasting multivariate realized stock market volatility

We present a new matrix-logarithm model of the realized covariance matrix of stock returns. The model uses latent factors which are functions of lagged volatility, lagged returns and other forecasting variables. The model has several advantages: it is parsimonious; it does not require imposing parameter restrictions; and, it results in a positive-definite estimated covariance matrix. We apply the model to the covariance matrix of size-sorted stock returns and find that two factors are sufficient to capture most of the dynamics.     

A Gaussian approximation scheme for computation of option prices in stochastic volatility models

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999–2002.     

Jump tails,extreme dependencies,and the distribution of stock returns

We provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices. Our estimates are based on in-fill asymptotics for directly identifying the jumps, together with Extreme Value Theory (EVT) approximations and methods-of-moments for assessing the tail decay parameters and tail dependencies. On implementing the procedures with a panel of intraday prices for a large cross-section of individual stocks and the S&P 500 market portfolio, we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy-tailed and close to symmetric, and show how the jump tail dependencies deduced from the high-frequency data together with the day-to-day variation in the diffusive volatility account for the “extreme” joint dependencies observed at the daily level.     

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow–Debreu securities with the S&P 500 index options data and the DAX index options data. The proposed Bayesian bandwidth selector represents a data-driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state-price density pioneered by Aït-Sahalia and Lo [Aït-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. The Journal of Finance, 53, 499, 547.]     

Testing for jumps when asset prices are observed with noise–a “swap variance” approach

This paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps. Formally, the test follows by a direct application of Itô’s lemma to the semi-martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments. Intuitively, the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps. Simulations show that the jump test has nice properties and is generally more powerful than the widely used bi-power variation test. An important feature of our test is that it can be applied–in analytically modified form–to noisy high frequency data and still retain power. As a by-product of our analysis, we obtain novel analytical results regarding the impact of noise on bi-power variation. An empirical illustration using IBM trade data is also included.     

Time-varying jump tails

We develop new methods for the estimation of time-varying risk-neutral jump tails in asset returns. In contrast to existing procedures based on tightly parameterized models, our approach imposes much fewer structural assumptions, relying on extreme-value theory approximations together with short-maturity options. The new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ, and importantly for the tail shape parameters to change over time. On implementing the procedures with a panel of S&P 500 options, our estimates clearly suggest the existence of highly statistically significant temporal variation in both of the tails. We further relate this temporal variation in the shape and the magnitude of the jump tails to the underlying return variation through the formulation of simple time series models for the tail parameters.     

Stale and Scale Effects in Markets-Based Accounting Research: Evidence from the Valuation of Dividends

Abstract

This study revisits prior research on the valuation of dividends in an accounting-based valuation framework. Using a battery of tests, we show that market value deflation is essential in market-based tests of dividend displacement and signalling because it controls for ‘stale’ information in addition to scale (size) differences across firms. For US firms, we show that after controlling for ‘stale’ information, the empirical association between dividends and market values switches from positive to negative. This switch is not explained by scale differences across firms. Further, we show that after controlling for staleness, the valuation of dividends remains positive for European firms. This result is explained by the relatively stronger association of dividends with future earnings in these settings (i.e. signalling). Lastly, our country-specific estimates of dividend valuation provide a potentially valuable index for studies aimed at examining the effects of accounting and securities regulation on information asymmetries in an international context.     

Semiparametric inference in a GARCH-in-mean model

A new semiparametric estimator for an empirical asset pricing model with general nonparametric risk-return tradeoff and GARCH-type underlying volatility is introduced. Based on the profile likelihood approach, it does not rely on any initial parametric estimator of the conditional mean function, and it is under stated conditions consistent, asymptotically normal, and efficient, i.e., it achieves the semiparametric lower bound. A sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of Conrad and Mammen (2008). An application to daily stock market returns suggests that the risk-return relation is indeed nonlinear.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.