New Economics Papers
on Financial Markets
Issue of 2008‒06‒27
fifteen papers chosen by

  1. The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets By Thomas Busch; Thomas Busch; Bent Jesper Christensen; Morten Ørregaard Nielsen
  2. Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model By Bent Jesper Christensen; Morten Ørregaard Nielsen; Jie Zhu
  3. Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities By Tim Bollerslev; Michael Gibson; Hao Zhou
  4. Real-Time Price Discovery in Global Stock, Bond and Foreign Exchange Markets By Torben G. Andersen; Tim Bollerslev; Francis X. Diebold; Clara Vega
  5. Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns By Torben G. Andersen; Tim Bollerslev; Per Houmann Frederiksen; Morten Ørregaard Nielsen
  6. A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects By Tim Bollerslev; Uta Kretschmer; Christian Pigorsch; George Tauchen
  7. Construction and Interpretation of Model-Free Implied Volatility By Torben G. Andersen; Oleg Bondarenko
  8. Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models By Torben G. Andersen; Luca Benzoni
  9. A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models By Mark Podolskij; Daniel Ziggel
  10. Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices By Peter Christoffersen; Kris Jacobs; Karim Mimouni
  11. Forward-Looking Betas By Peter Christoffersen; Kris Jacobs; Gregory Vainberg
  12. Option Valuation with Long-run and Short-run Volatility Components By Peter Christoffersen; Kris Jacobs; Chayawat Ornthanalai; Yintian Wang
  13. Option Pricing using Realized Volatility By Lars Stentoft
  14. Pricing Volatility of Stock Returns with Volatile and Persistent Components By Jie Zhu
  15. Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks By Viktor Todorov; Tim Bollerslev

  1. By: Thomas Busch; Thomas Busch; Bent Jesper Christensen; Morten Ørregaard Nielsen (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We study the forecasting of future realized volatility in the stock, bond, and for- eign exchange markets, as well as the continuous sample path and jump components of this, from variables in the information set, including implied volatility backed out from option prices. Recent nonparametric statistical techniques of Barndor¤-Nielsen & Shephard (2004, 2006) are used to separate realized volatility into its continuous and jump components, which enhances forecasting performance, as shown by Andersen, Bollerslev & Diebold (2005). We generalize the heterogeneous autoregressive (HAR) model of Corsi (2004) to include implied volatility as an additional regressor, and to the separate forecasting of the realized components. We also introduce a new vector HAR (VecHAR) model for the resulting simultaneous system, controlling for possible endogeneity issues in the forecasting equations. We show that implied volatility con- tains incremental information about future volatility relative to both continuous and jump components of past realized volatility. Indeed, in the foreign exchange market, implied volatility completely subsumes the information content of daily, weekly, and monthly realized volatility measures, when forecasting future realized volatility or its continuous component. In addition, implied volatility is an unbiased forecast of future realized volatility in the foreign exchange and stock markets. Perhaps surprisingly, the jump component of realized return volatility is, to some extent, predictable, and options appear to be calibrated to incorporate information about future jumps in all three markets.
    Keywords: Bipower variation, HAR, Heterogeneous Autoregressive Model, implied volatility, jumps, options, realized volatility, VecHAR, volatility forecasting
    JEL: C22 C32 F31 G1
    Date: 2007–06–06
  2. By: Bent Jesper Christensen; Morten Ørregaard Nielsen; Jie Zhu (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the S&P 500 index which documents the empirical relevance of our model.
    Keywords: FIEGARCH, financial leverage, GARCH, long memory, risk-return tradeoff, stock returns, volatility feedback
    JEL: C22
    Date: 2007–06–12
  3. By: Tim Bollerslev; Michael Gibson; Hao Zhou (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.
    Keywords: Stochastic Volatility Risk Premium, Model-Free Implied Volatility, Model-Free Realized Volatility, Black-Scholes, GMM Estimation, Return Predictability
    JEL: G12 G13 C51 C52
    Date: 2007–08–16
  4. By: Torben G. Andersen; Tim Bollerslev; Francis X. Diebold; Clara Vega (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: Using a unique high-frequency futures dataset, we characterize the response of U.S., German and British stock, bond and foreign exchange markets to real-time U.S. macroeconomic news. We find that news produces conditional mean jumps, hence high-frequency stock, bond and exchange rate dynamics are linked to fundamentals. Equity markets, moreover, react differently to news depending on the stage of the business cycle, which explains the low correlation between stock and bond returns when averaged over the cycle. Hence our results qualify earlier work suggesting that bond markets react most strongly to macroeconomic news, in particular, when conditioning on the state of the economy, the equity and foreign exchange markets appear equally responsive. Finally, we also document important contemporaneous links across all markets and countries, even after controlling for the effects of macroeconomic news.
    Keywords: Asset Pricing, Macroeconomic News Announcements, Financial Market Linkages, Market Microstructure, High-Frequency Data, Survey Data, Asset Return Volatility, Forecasting
    JEL: F3 F4 G1 C5
    Date: 2007–08–16
  5. By: Torben G. Andersen; Tim Bollerslev; Per Houmann Frederiksen; Morten Ørregaard Nielsen (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We provide an empirical framework for assessing the distributional properties of daily specu- lative returns within the context of the continuous-time modeling paradigm traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non-parametric jump detection statistics constructed from high-frequency intra- day data. A sequence of relatively simple-to-implement moment-based tests involving various transforms of the daily returns speak directly to the import of different features of the under- lying continuous-time processes that might have generated the data. As such, the tests may serve as a useful diagnostic tool in the specification of empirically more realistic asset pricing models. Our results are also directly related to the popular mixture-of-distributions hypoth- esis and the role of the corresponding latent information arrival process. On applying our sequential test procedure to the thirty individual stocks in the Dow Jones Industrial Average index, the data suggest that it is important to allow for both time-varying diffusive volatility, jumps, and leverage effects in order to satisfactorily describe the daily stock price dynamics. At a broader level, the empirical results also illustrate how the realized variation measures and high-frequency sampling schemes may be used in eliciting important distributional features and asset pricing implications more generally.
    Keywords: Return distributions, continuous-time models, mixture-of-distributions hypothesis, financial-time sampling, high-frequency data, volatility signature plots, realized volatilities, jumps, leverage and volatility feedback effects
    JEL: C1 G1
    Date: 2007–08–16
  6. By: Tim Bollerslev; Uta Kretschmer; Christian Pigorsch; George Tauchen (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easyto- implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and L´evy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.
    Keywords: Realized volatility, Bipower variation, Jumps, Leverage effect, Simultaneous equation model
    JEL: C1 C3 C5 G1
    Date: 2007–08–16
  7. By: Torben G. Andersen; Oleg Bondarenko (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the VIX index is computed through a tail-truncation which renders it more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and hence estimate the corresponding volatility measures, under the standard Black-Scholes model. Finally, we undertake the first empirical exploration of the CIV measures in the literature. Our results indicate that the measure can help us refine and systematize the information embedded in the derivatives markets. As such, the CIV measure may serve as a tool to facilitate empirical analysis of both volatility forecasting and volatility risk pricing across distinct future states of the world for diverse asset categories and time horizons.
    Keywords: Model-Free Implied Volatility, Corridor Implied Volatility, Realized Volatility, VIX, Volatility Forecasting, Risk-Neutral Density
    JEL: C53 G12 G13
    Date: 2007–09–17
  8. By: Torben G. Andersen; Luca Benzoni (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most `a±ne' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of ¯xed-maturity zero-coupon bonds (`realized yield volatility') through the use of high-frequency data. We ¯nd that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross- section of yields. We conclude that a broad class of a±ne di®usive, Gaussian-quadratic and a±ne jump-di®usive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for speci¯cation testing and (parametric) model selection within the term structure literature.
    Date: 2007–09–17
  9. By: Mark Podolskij; Daniel Ziggel (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We propose a new test for the parametric form of the volatility function in continuous time diffusion models of the type dXt = a(t,Xt)dt + s(t,Xt)dWt. Our approach involves a range-based estimation of the integrated volatility and the integrated quarticity, which are used to construct the test statistic. Under rather weak assumptions on the drift and volatility we prove weak convergence of the test statistic to a centered mixed Gaussian distribution. As a consequence we obtain a test, which is consistent for any fixed alternative. Moreover, we present a parametric bootstrap procedure which provides a better approximation of the distribution of the test statistic. Finally, it is demonstrated by means of Monte Carlo study that the range-based test is more powerful than the return-based test when comparing at the same sampling frequency.
    Keywords: Bipower Variation, Central Limit Theorem, Diffusion Models, Goodness-Of- Fit Testing, High-Frequency Data, Integrated Volatility, Range-Based Bipower Variation, Semimartingale Theory
    JEL: C12 C14
    Date: 2007–09–19
  10. By: Peter Christoffersen; Kris Jacobs; Karim Mimouni (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on S&P500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared errors in- and out-of-sample.
    Keywords: Stochastic volatility, option valuation, particle filtering, skewness, kurtosis, mean reversion
    JEL: G12
    Date: 2007–11–15
  11. By: Peter Christoffersen; Kris Jacobs; Gregory Vainberg (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: Few issues are more important for finance practice than the computation of market betas. Existing approaches compute market betas using historical data. While these approaches differ in terms of statistical sophistication and the modeling of the time-variation in the betas, they are all backward-looking. This paper introduces a radically different approach to estimating market betas. Using the tools in Bakshi and Madan (2000) and Bakshi, Kapadia and Madan (2003) we employ the information embedded in the prices of individual stock options and index options to compute our forward-looking market beta at the daily frequency. This beta can be computed using option data for a single day, and is able to reflect sudden changes in the structure of the underlying company. Based on an empirical investigation of daily cross-sections of option contracts on thirty underlying companies, we conclude that these forward-looking betas contain information relevant for forecasting future betas that is not contained in historical betas.
    Keywords: market beta, CAPM, historical, forward-looking, option-implied, capital budgeting, event studies, model-free moments
    JEL: G12
    Date: 2007–11–22
  12. By: Peter Christoffersen; Kris Jacobs; Chayawat Ornthanalai; Yintian Wang (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: This paper presents a new model for the valuation of European options, in which the volatility of returns consists of two components. One of these components is a long-run component, and it can be modeled as fully persistent. The other component is short-run and has a zero mean. Our model can be viewed as an affine version of Engle and Lee (1999), 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 Poissonnormal 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.
    Keywords: Volatility term structure; GARCH; out-of-sample
    JEL: G12
    Date: 2008–02–18
  13. By: Lars Stentoft (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate dynamics to be used for option pricing purposes in this framework, and we show that our model explains some of the mispricings found when using traditional option pricing models based on interdaily data. We then show explicitly that a Generalized Autoregressive Conditional Heteroskedastic model with Normal Inverse Gaussian distributed innovations is the corresponding benchmark model when only daily data is used. Finally, we perform an empirical analysis using stock options for three large American companies, and we show that in all cases our model performs significantly better than the corresponding benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes.
    Keywords: Option Pricing, Realized Volatility, Stochastic Volatility, GARCH
    JEL: C22 C53 G13
    Date: 2008–03–03
  14. By: Jie Zhu (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: In this paper a two-component volatility model based on the component's first moment is introduced to describe the dynamic of speculative return volatility. The two components capture the volatile and persistent part of volatility respectively. Then the model is applied to 10 Asia-Pacific stock markets. Their in-mean effects on return are also tested. The empirical results show that the persistent component accounts much more for volatility dynamic process than the volatile component. However the volatile component is found to be a significant pricing factor of asset returns for most markets, a positive or risk-premium effect exists between return and the volatile component, yet the persistent component is not significantly priced for return dynamic process.
    Keywords: Risk, Return, In-mean effect, Volatile, Persistent, Innovations
    JEL: C14 G12 G15
    Date: 2008–03–05
  15. By: Viktor Todorov; Tim Bollerslev (School of Economics and Management, University of Aarhus, Denmark)
    Abstract: We provide a new theoretical framework for disentangling and estimating sensitivity towards systematic diffusive and jump risks in the context of factor pricing 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. In addition to establish- ing consistency of our estimators, we also derive Central Limit Theorems characterizing their asymptotic distributions. In an empirical application of the new procedures using high-frequency data for forty individual stocks and an aggregate market portfolio, we find the estimated diffusive and jump betas with respect to the market to be quite dif- ferent for many of the stocks. Our findings have direct and important implications for empirical asset pricing finance and practical portfolio and risk management decisions.
    Keywords: Factor models, systematic risk, common jumps, high-frequency data, realized variation
    JEL: C13 C14 G10 G12
    Date: 2007–08–16

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