The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

New evidence on the implied-realized volatility relation

We consider the relation between the volatility implied in an option's price and the subsequently realized volatility. Earlier studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. More recently, Christensen and Prabhala find that implied volatility in at-the-money one-month OEX call options on the S&P 100 index in fact is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. In this paper, the robustness of the unbiasedness and efficiency result is extended to a more recent period covering April 1993 to February 1997. As a new contribution, implied volatility is constructed as a trade weighted average of implied volatilities from both in-the-money and out-of-the-money options and both puts and calls. We run a horse race between implied call, implied put, and historical return volatility. Several robustness checks, including a new simultaneous equation approach, underscore our conclusion, that implied volatility is an efficient forecast of realized return volatility.     

Option valuation with long-run and short-run volatility components

This paper presents a new model for the valuation of European options, in which the volatility of returns consists of two components. One is a long-run component and can be modeled as fully persistent. The other is short-run and has a zero mean. Our model can be viewed as an affine version of Engle and Lee [1999. A permanent and transitory component model of stock return volatility. In: Engle, R., White, H. (Eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger. Oxford University Press, New York, pp. 475–497], allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature, and it fits options better than a model that combines conditional heteroskedasticity and Poisson–normal jumps. The component model's superior performance is partly due to its improved ability to model the smirk and the path of spot volatility, but its most distinctive feature is its ability to model the volatility term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.     

The determination and international transmission of stock market volatility

This paper extends the literature on low-frequency analysis of the causes and transmission of stock market volatility. It uses end-monthly data on stock market returns, interest rates, exchange rates, inflation, and industrial production for five countries (Britain, France, Germany, Japan, and the US) from July 1973 to December 1994. Efficient portfolios of world, European, and Japanese/US equity are first constructed, the existence of multivariate cointegrating relationships between them is demonstrated, and the transmission of conditional volatility between them is described. The transmission of conditional volatility from world equity markets and national business cycle variables to national stock markets is then modeled. Among the main findings are: first, world equity market volatility is caused mostly by volatility in Japanese/US markets and transmitted to European markets, and second, changes in the volatility of inflation are associated with changes of the opposite sign in stock market volatility in all markets where a significant effect is found to exist. To the extent that the volatility of inflation is positively related to its level, this implies that low inflation tends to be associated with high stock market volatility.     

There's more to volatility than volume

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyse recent results of Ane and Geman (2000 Ane, T and Geman, H. 2000. Order flow, transaction clock, and normality of asset returns. J. Finance, 55(5): 2259–2284. [Crossref], [Web of Science ®] , [Google Scholar]: J. Finance, 55, 2259–2284) and Gabaix et al. (2003 Gabaix, X, Gopikrishnan, P, Plerou, V and Stanley, H.E. 2003. A theory of power-law distributions in financial market fluctuations. Nature, 423: 267–270. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]: Nature, 423, 267–270), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.     

Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility ‘skew’ or ‘smile’. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.     

Regime-switching volatility of six East Asian emerging markets

This paper investigates regime-switching behaviour in the return-generating processes of six East Asian emerging stock markets over the period from 1970 to 2004 and examines the specific characteristics of each regime by utilizing Markov-switching variance models. The results show very strong evidence of more than one regime in each of these stock markets. In addition, the conditional probabilities of each regime derived from the model provide mixed evidence regarding the impact of financial liberalization on return volatility.     

Stock volatility predictability in bull and bear markets

The recent literature on stock return predictability suggests that it varies substantially across economic states, being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, in this paper, we use a large data set of high-frequency data on individual stocks and a few popular time-series volatility models to comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, over all but the shortest horizons, the volatility forecast accuracy is higher when the market is in a bear state. This difference increases as the forecast horizon lengthens. Our study concludes that stock volatility predictability is strongest during bad economic times, proxied by bear market states.     

Modeling volatility and changes in the swap spread

We investigate the determinants of changes in U.S. interest rate swap spreads using a model that explicitly allows for volatility interactions between swaps of different terms to maturity. Changes in the swap spread are found to be positively related to interest rate volatility, to changes in the default risk premium in the corporate bond market, and to changes in the liquidity premium for government securities. Swap spread changes are negatively related to changes in the level of interest rates and changes in the slope of the term structure. We also find that there is a strong and significant volatility interaction among spreads for swaps of different maturities and that the process for the conditional variance of the spread is highly persistent across all maturities.     

Macroeconomic fundamentals,jump dynamics and expected volatility

In this paper, we develop a new volatility model capturing the effects of macroeconomic variables and jump dynamics on the stock volatility. The proposed GARCH-Jump-MIDAS model is applied to the S&P 500 index. Our in-sample results indicate that macroeconomic activities have important impacts on aggregate market volatility. Out-of-sample evidence suggests that our model with macroeconomic variables significantly outperform a wide range of competitors including the original GARCH(1,1), GARCH-MIDAS and GJR-A-MIDAS models. The volatility timing results also show that the information from jumps and macroeconomic activity is helpful for improving the portfolio performance.     

Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

Intraday volatility and periodicity in the Malaysian stock returns

Many empirical studies using high-frequency intraday data from a variety of markets indicate that PGARCH models give superior return volatility forecasts than those produced from standard GARCH models. This paper investigates into modelling approaches of four versions of PGARCH models of high-frequency data of Bursa Malaysia, in particular where the intraday volatility of double U-shaped pattern. It is examined through half-hourly dummy variables, quarterly-hourly dummy variables, Fourier Functional Form (FFF) based variables and spline-based variables. The non-periodic GARCH models, i.e., GARCH, EGARCH and TARCH are used for comparison of performance of best fit. The analysis show that among the four versions of PGARCH models, the half-dummy and the spline-based versions perform the best. EGARCH produced consistently superior results to other GARCH specifications.     

Testing for volatility spillover between the British pound and the euro

This paper examines volatility spillover between two nominal U.S. dollar exchange rates: the British pound and the euro. Using the residual cross-correlation approach, we observe that the euro Granger-causes the British pound in variance, whereas the British pound does not Granger-cause the euro in variance. Our findings support unidirectional volatility spillover from the euro to the British pound; thus, the euro volatility has a one-sided impact on the British pound volatility. Moreover, the findings suggest that euro traders succeed in the efficient processing of information derived from the British pound.     

The euro and pound volatility dynamics: An investigation from conditional jump process

This paper investigates the variations of the volatility of euro and pound after the introduction of euro. A GARJI model is employed to analyze the impact of the news arrivals on the exchange rate volatility. The results are robust to the data-splitting schemes and indicate: (1) the conditional variance of euro is larger than that of pound. (2) The stability of euro exchange rates has made progress in recent years, which is accomplished by the decreases in the jump innovations. This paper supports the arguments on the determinants of exchange rate stability claimed by Mundell (1998) and Mussa (2000).     

Bayesian testing volatility persistence in stochastic volatility models with jumps

Whether or not there is a unit root persistence in volatility of financial assets has been a long-standing topic of interest to financial econometricians and empirical economists. The purpose of this article is to provide a Bayesian approach for testing the volatility persistence in the context of stochastic volatility with Merton jump and correlated Merton jump. The Shanghai Composite Index daily return data is used for empirical illustration. The result of Bayesian hypothesis testing strongly indicates that the volatility process doesn’t have unit root volatility persistence in this stock market.     

Trading volume and stock market volatility: The Polish case

Relying on the mixture of distributions hypothesis (MDH), this paper investigates the relationship between daily returns and trading volume for 20 Polish stocks. Our empirical results show that in the majority of cases volatility persistence tends to disappear when trading volume is included in the conditional variance equation, which is in agreement with the findings of studies on developed stock markets. However, we cannot confirm the testable implications of the MDH in all cases, which indicates that future research on the causes and modeling of Polish stock market volatility is necessary.     

Contemporaneous intraday volume, option, and futures volatility transmissions across parallel markets

The primary objective of this article is to investigate volatility transmission across three parallel markets operating on the Sydney Futures Exchange (SFE), both within and out of sample. Half-hourly observations are sampled from transaction data for the share price index (SPI) futures, SPI futures options, and 90-day bank accepted bill (BAB) futures markets, and the analysis is carried out using the simultaneous volatility (SVL) system of equations as well as competing volatility models. The results confirm the poor ability of GARCH models to fit intraday data. This study also applies an artificial nesting procedure to evaluate the out-of-sample volatility forecasts. Implied volatility has very limited (if any) predictive power when evaluated in isolation, whereas the SVL model with implied volatility embedded provides incremental information relative to competing model forecasts.     

The empirical similarity approach for volatility prediction

In this paper we adapt the empirical similarity (ES) concept for the purpose of combining volatility forecasts originating from different models. Our ES approach is suitable for situations where a decision maker refrains from evaluating success probabilities of forecasting models but prefers to think by analogy. It allows to determine weights of the forecasting combination by quantifying distances between model predictions and corresponding realizations of the process of interest as they are perceived by decision makers. The proposed ES approach is applied for combining models in order to forecast daily volatility of the major stock market indices.     

Using information quality for volatility model combinations

This paper proposes updated methodology for volatility model combinations which account for the informational content of innovations. An adaptive measure of information quality serves for the selection of model weights in order to improve daily volatility forecasts. The information quality proxy is related to the size of unexpected shocks in the volatility process. Our approach is illustrated in an empirical study with German stock market data.     

Structural effects and spillovers in HSIF, HSI and S&P500 volatility

We adopt a BEKK-GARCH framework and employ a systematic approach to jointly examine structural breaks in the Hong Kong cash index and index futures volatility and volatility spillovers from the S&P 500 cash and futures. Multiple switching dummy variables are included in the variance equations to test for any structural changes in the autoregressive volatility structure due to the events that have taken place in the Hong Kong market. Abolishment of the up-tick rule, increase of initial margins and electronic trading of the Hang Seng Index Futures (HSIF) are found to have significant impact when US market spillovers are excluded from a restricted model. Volatility spillovers from the US market are found to have a significant impact and account for some mis-specification in the restricted model.