Separating microstructure noise from volatility

There are two variance components embedded in the returns constructed using high frequency asset prices: the time-varying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components.     

Robust estimation of intraweek periodicity in volatility and jump detection

Opening, lunch and closing of financial markets induce a periodic component in the volatility of high-frequency returns. We show that price jumps cause a large bias in the classical periodicity estimators and propose robust alternatives. We find that accounting for periodicity greatly improves the accuracy of intraday jump detection methods. It increases the power to detect the relatively small jumps occurring at times for which volatility is periodically low and reduces the number of spurious jump detections at times of periodically high volatility. We use the series of detected jumps to estimate robustly the long memory parameter of the squared EUR/USD, GBP/USD and YEN/USD returns.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997

Foreign exchange (FX) pricing processes are nonstationary: Their frequency characteristics are time dependent. Most do not conform to Geometric Brownian Motion (GBM), because they exhibit a scaling law with Hurst exponents between zero and 0.5 and fractal dimensions between 1.5 and 2. Wavelet multiresolution analysis (MRA), with Haar wavelets, is used to analyze these time and scale dependencies (self-similarity) of intraday Asian currency spot exchange rates. We use the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, and Thailand) and, for comparison, of Germany for the crisis period May 1, 1998-August 31, 1997, provided by Telerate (U.S. dollar is the numéraire). Their time-scale-dependent spectra, which are localized in time, are observed in wavelet scalograms. The FX increments are characterized by the irregularity of their singularities. Their degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the global fractal dimension, relative stability, and long-term dependence, or long-term memory, of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all investigated FX markets show antipersistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen (JPY) are ultraefficient in the sense of being most antipersistent or “fast mean-reversing.” This is a surprising result because most financial analyst either assume neutral or persistent behavior in the financial markets, based on earlier research by Granger in the 1960s. This is a pedagogical paper explaining the most rational methodology for the identification of long-term memory in financial time series.     

Forecasting the fragility of the banking and insurance sectors

Linkages between banks and insurance companies are important when forecasting the fragility of the banking and insurance sectors. We propose a novel empirical framework that allows us to estimate unobserved linkages in panel data sets that contain observed regressors. We find that taking unobserved common factors into account reduces the root mean square forecasts error of firm specific forecasts by up to 9%, of system forecasts by up to 14%, and by up to 39% for systemic forecasts of more distressed firms relative to a model based on observed variables only. Estimates of the factor loadings suggest that the correlation of financial institutions has been relatively stable over the forecast period.     

The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.     

Risk and return: Long-run relations,fractional cointegration,and return predictability

Univariate dependencies in market volatility, both objective and risk neutral, are best described by long-memory fractionally integrated processes. Meanwhile, the ex post difference, or the variance swap payoff reflecting the reward for bearing volatility risk, displays far less persistent dynamics. Using intraday data for the Standard & Poor's 500 and the volatility index (VIX), coupled with frequency domain methods, we separate the series into various components. We find that the coherence between volatility and the volatility-risk reward is the strongest at long-run frequencies. Our results are consistent with generalized long-run risk models and help explain why classical efforts of establishing a naïve return-volatility relation fail. We also estimate a fractionally cointegrated vector autoregression (CFVAR). The model-implied long-run equilibrium relation between the two variance variables results in nontrivial return predictability over interdaily and monthly horizons, supporting the idea that the cointegrating relation between the two variance measures proxies for the economic uncertainty rewarded by the market.     

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.     

Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas

We propose to model the joint distribution of bid-ask spreads and log returns of a stock portfolio by using Autoregressive Conditional Double Poisson and GARCH processes for the marginals and vine copulas for the dependence structure. By estimating the joint multivariate distribution of both returns and bid-ask spreads from intraday data, we incorporate the measurement of commonalities in liquidity and comovements of stocks and bid-ask spreads into the forecasting of three types of liquidity-adjusted intraday Value-at-Risk (L-IVaR). In a preliminary analysis, we document strong extreme comovements in liquidity and strong tail dependence between bid-ask spreads and log returns across the firms in our sample thus motivating our use of a vine copula model. Furthermore, the backtesting results for the L-IVaR of a portfolio consisting of five stocks listed on the NASDAQ show that the proposed models perform well in forecasting liquidity-adjusted intraday portfolio profits and losses.     

Overnight information and stochastic volatility: A study of European and US stock exchanges

This paper provides a comprehensive evaluation of the predictive ability of information accumulated during nontrading hours for a set of European and US stock indexes. We introduce a stochastic volatility model, which conditions on lagged overnight information, distinguishes between the nontrading periods of weeknights, weekends, holidays and long weekends, and allows for an asymmetric leverage effect on the impact of overnight news. We implement Bayesian methods for estimation and ranking of the empirical models, and find two key results: (i) there is substantial predictive ability in financial information accumulated during nontrading hours; and (ii) the performance of stochastic volatility models improves considerably by separating the asymmetric impact of positive and negative news made available over weeknights, weekends, holidays and long weekends.     

The volatility effect of futures trading: Evidence from LSE traded stocks listed as individual equity futures contracts on LIFFE

This study investigates the impact of LIFFE's introduction of individual equity futures contracts on the risk characteristics of the underlying stocks trading on the LSE. We employ the Fama and French three-factor model (TFM) to measure the change in the systematic risk of the underlying stocks which arises subsequent to the introduction of futures contracts. A GJR-GARCH(1,1) specification is used to test whether the futures contract listing affects the permanent and/or the transitory component of the residual variance of returns, and a control sample methodology isolates changes in the risk components that may be caused by factors other than futures contract innovation. The observed increase (decrease) in the impact of current (old) news on the residual variance implies that futures contract listing enhances stock market efficiency. There is no evidence that futures innovation impacts on either the systematic risk or the permanent component of the residual variance of returns.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

Some nonstandard stochastic volatility models and their estimation using structured hidden Markov models

We introduce a number of nonstandard stochastic volatility (SV) models and examine their performance when applied to the series of daily returns on several stocks listed on the New York Stock Exchange. The nonstandard models under investigation extend both the observation process and the volatility-generating process of basic SV models. In particular, we consider dependent as well as independent mixtures of autoregressive components as the log-volatility process, and include in the observation equation a lower bound on the volatility. We also consider an experimental SV model that is based on conditionally gamma-distributed volatilities.Our estimation method is based on the fact that an SV model can be approximated arbitrarily accurately by a hidden Markov model (HMM), whose likelihood is easy to compute and to maximize. The method is close, but not identical, to those of Fridman and Harris (1998), Bartolucci and De Luca (2001, 2003) and Clements et al. (2006), and makes explicit the useful link between HMMs and the methods of those authors. Likelihood-based estimation of the parameters of SV models is usually regarded as challenging because the likelihood is a high-dimensional multiple integral. The HMM approximation is easy to implement and particularly convenient for fitting experimental extensions and variants of SV models such as those we introduce here. In addition, and in contrast to the case of SV models themselves, simple formulae are available for the forecast distributions of HMMs, for computing appropriately defined residuals, and for decoding, i.e. estimating the volatility of the process.     

Modeling structural changes in the volatility process

GARCH-type models have been very successful in describing the volatility dynamics of financial return series for short periods of time. However, the time-varying behavior of investors, for example, may cause the structure of volatility to change and the assumption of stationarity is no longer plausible. To deal with this issue, the current paper proposes a conditional volatility model with time-varying coefficients based on a multinomial switching mechanism. By giving more weight to either the persistence or shock term in a GARCH model, conditional on their relative ability to forecast a benchmark volatility measure, the switching reinforces the persistent nature of the GARCH model. The estimation of this benchmark volatility targeting or BVT-GARCH model for Dow 30 stocks indicates that the switching model is able to outperform a number of relevant GARCH setups, both in- and out-of-sample, also without any informational advantages.     

Does implied volatility provide any information beyond that captured in model-based volatility forecasts?

This paper contributes to our understanding of the informational content of implied volatility. Here we examine whether the S&P 500 implied volatility index (VIX) contains any information relevant to future volatility beyond that available from model based volatility forecasts. It is argued that this approach differs from the traditional forecast encompassing approach used in earlier studies. The findings indicate that the VIX index does not contain any such additional information relevant for forecasting volatility.     

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.     

Modelling and forecasting short-term interest rate volatility: A semiparametric approach

This paper employs a semiparametric procedure to estimate the diffusion process of short-term interest rates. The Monte Carlo study shows that the semiparametric approach produces more accurate volatility estimates than models that accommodate asymmetry, level effect and serial dependence in the conditional variance. Moreover, the semiparametric approach yields robust volatility estimates even if the short rate drift function and the underlying innovation distribution are misspecified. Empirical investigation with the U.S. three-month Treasury bill rates suggests that the semiparametric procedure produces superior in-sample and out-of-sample forecast of short rate changes volatility compared with the widely used single-factor diffusion models. This forecast improvement has implications for pricing interest rate derivatives.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Efficient tests of stock return predictability

Conventional tests of the predictability of stock returns could be invalid, that is reject the null too frequently, when the predictor variable is persistent and its innovations are highly correlated with returns. We develop a pretest to determine whether the conventional t-test leads to invalid inference and an efficient test of predictability that corrects this problem. Although the conventional t-test is invalid for the dividend–price and smoothed earnings–price ratios, our test finds evidence for predictability. We also find evidence for predictability with the short rate and the long-short yield spread, for which the conventional t-test leads to valid inference.