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on Market Microstructure |
| By: | Ingmar Nolte; Valeri Voev (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We propose a unified framework for estimating integrated variances and covariances based on simple OLS regressions, allowing for a general market microstructure noise specification. We show that our estimators can outperform, in terms of the root mean squared error criterion, the most recent and commonly applied estimators, such as the realized kernels of Barndorff-Nielsen, Hansen, Lunde & Shephard (2006), the two-scales realized variance of Zhang, Mykland & Aït-Sahalia (2005), the Hayashi & Yoshida (2005) covariance estimator, and the realized variance and covariance with the optimal sampling frequency derived in Bandi & Russell (2005a) and Bandi & Russell (2005b). For a realistic trading scenario, the efficiency gains resulting from our approach are in the range of 35% to 50%. |
| Keywords: | High frequency data, Realized volatility and covariance, Market microstructure |
| JEL: | G10 F31 C32 |
| Date: | 2008–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-31&r=mst |
| By: | Silja Kinnebrock; Mark Podolskij (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | This paper introduces a new estimator to measure the ex-post covariation between high-frequency financial time series under market microstructure noise. We provide an asymptotic limit theory (including feasible central limit theorems) for standard methods such as regression, correlation analysis and covariance, for which we obtain the optimal rate of convergence. We demonstrate some positive semidefinite estimators of the covariation and construct a positive semidefinite estimator of the conditional covariance matrix in the central limit theorem. Furthermore, we indicate how the assumptions on the noise process can be relaxed and how our method can be applied to non-synchronous observations. We also present an empirical study of how high-frequency correlations, regressions and covariances change through time. |
| Keywords: | Central Limit Theorem, Diffusion Models, Market Microstructure Noise, Non-synchronous Trading, High-Frequency Data, Semimartingale Theory |
| Date: | 2008–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-23&r=mst |
| By: | Mark Podolskij; Mathias Vetter (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower variation is proven. Under further assumptions we prove stable convergence of our estimates with the optimal rate n-1/4. Moreover, we construct estimates which are robust to finite activity jumps. |
| Keywords: | Bipower Variation, Central Limit Theorem, Finite Activity Jumps, High-Frequency Data, Integrated Volatility, Microstructure Noise, Semimartingale Theory, Subsampling |
| JEL: | C10 C13 C14 |
| Date: | 2007–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-27&r=mst |
| By: | Torben G. Andersen; Tim Bollerslev; Xin Huang (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability is well described by an approximate long-memory HAR-GARCH model, while the overnight returns may be modelled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Lastly, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility. |
| Keywords: | Stochastic Volatility, Realized Variation, Bipower Variation, Jumps, Hazard Rates, Overnight Volatility |
| JEL: | C1 G1 C2 |
| Date: | 2007–08–16 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-14&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-20&r=mst |
| By: | Mark Podolskij; Mathias Vetter (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We consider a new class of estimators for volatility functionals in the setting of frequently observed Itô diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Itô semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale. |
| Keywords: | Bipower Variation, Central Limit Theorem, High-Frequency Data, Microstructure Noise, Quadratic Variation, Semimartingale Theory, Test for Jumps |
| JEL: | C10 C13 C14 |
| Date: | 2008–05–26 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-25&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-21&r=mst |
| By: | Guillaume Rocheteau; Ricardo Lagos |
| Abstract: | We develop a search-theoretic model of financial intermediation and use it to study how trading frictions affect the distribution of asset holdings, asset prices, efficiency and standard measures of liquidity. A distinctive feature of our theory is that it allows for unrestricted asset holdings, so market participants can accommodate trading frictions by adjusting their asset positions. We show that these individual responses of asset demands constitute a fundamental feature of illiquid markets: they are a key determinant of bid-ask spreads, trade volume and trading delays—all the dimensions of market liquidity that search-based theories seek to explain. |
| Keywords: | Liquidity (Economics) ; Over-the-counter markets ; Investments |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwp:0804&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-22&r=mst |
| By: | Almut Veraart (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | Recent research has focused on modelling asset prices by Itô semimartingales. In such a modelling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realised variance and realised multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realised variance and realised multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory which is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory. |
| Keywords: | Quadratic variation, Itô semimartingale, stochastic volatility, jumps, realised variance, realised multipower variation, high–frequency data |
| JEL: | C13 C14 G10 G12 |
| Date: | 2008–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-17&r=mst |
| By: | Marwan Izzeldin; Ana-Maria Fuertes; Elena Kalotychou |
| Abstract: | Several recent studies advocate the use of nonparametric estimators of daily price vari- ability that exploit intraday information. This paper compares four such estimators, realised volatility, realised range, realised power variation and realised bipower variation, by examining their in-sample distributional properties and out-of-sample forecast ranking when the object of interest is the conventional conditional variance. The analysis is based on a 7-year sample of transaction prices for 14 NYSE stocks. The forecast race is conducted in a GARCH framework and relies on several loss functions. The realized range fares relatively well in the in-sample .t analysis, for instance, regarding the extent to which it brings normality in returns. However, overall the realised power variation provides the most accurate 1-day-ahead forecasts. Fore- cast combination of all four intraday measures produces the smallest forecast errors in about half of the sampled stocks. A market conditions analysis reveals that the additional use of intraday data on day t .. 1 to forecast volatility on day t is most advantageous when day t is a low volume or an up-market day. The results have implications for value-at-risk analysis. |
| Keywords: | C53; C32; C14. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:005439&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-09&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-15&r=mst |
| By: | Ricardo Lagos; Guillaume Rocheteau; Pierre-Olivier Weill |
| Abstract: | We study the dynamics of liquidity provision by dealers during an asset market crash, described as a temporary negative shock to investors aggregate asset demand. We consider a class of dynamic market settings where dealers can trade continuously with each other, while trading between dealers and investors is subject to delays and involves bargaining. We derive conditions on fundamentals, such as preferences, market structure and the characteristics of the market crash (e.g., severity, persistence) under which dealers provide liquidity to investors following the crash. We also characterize the conditions under which dealers incentives to provide liquidity are consistent with market efficiency. |
| JEL: | C78 D83 E44 G1 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14119&r=mst |
| 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 + (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. We also provide a test for neighborhood hypotheses. 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: | 2008–05–14 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-22&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-26&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-13&r=mst |
| By: | Tim Bollerslev; Hao Zhou (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We find that the difference between implied and realized variation, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low) future returns. The magnitude of the return predictability of the variance risk premium easily dominates that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread, and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E ratio results in an R2 for the quarterly returns of more than twenty-five percent. The results depend crucially on the use of “model-free”, as opposed to standard Black-Scholes, implied variances, and realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings suggest that temporal variation in both risk-aversion and volatility-risk play an important role in determining stock market returns. |
| Keywords: | Return Predictability, Implied Variance, Realized Variance, Equity Risk Premium, Variance Risk Premium, Time-Varying Risk Aversion |
| JEL: | G12 G14 |
| Date: | 2007–08–16 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-17&r=mst |
| By: | Mark Podolskij; Daniel Ziggel (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | In this paper we propose a test to determine whether jumps are present in a discretely sampled process or not. We use the concept of truncated power variation to construct our test statistics for (i) semimartingale models and (ii) semimartingale models with noise. The test statistics converge to innity if jumps are present and have a normal distribution otherwise. Our method is valid (under very weak assumptions) for all semimartingales with absolute continuous characteristics and rather general model for the noise process. We nally implement the test and present the simulation results. Our simulations suggest that for semimartingale models the new test is much more powerful then tests proposed by Barndorff-Nielsen and Shephard (2006) and At-Sahalia and Jacod (2008). |
| Keywords: | Central Limit Theorem, High-Frequency Data, Microstructure Noise, Semimartingale Theory, Tests for Jumps, Truncated Power Variation |
| JEL: | C10 C13 C14 |
| Date: | 2008–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-34&r=mst |
| By: | Ole E. Barndorff-Nielsen; José Manuel Corcuera; Mark Podolskij (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We develop the asymptotic theory for the realised power variation of the processes X = f • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process f we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the H¨older index of the path of f, we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu & Nualart (2005), Nualart & Peccati (2005) and Peccati & Tudor (2005), for sequences of random variables which admit a chaos representation. |
| Keywords: | Central Limit Theorem, Chaos Expansion, Gaussian Processes, High-Frequency Data, Multiple Wiener-Itô Integrals, Power Variation |
| JEL: | C10 C13 C14 |
| Date: | 2007–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-42&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-25&r=mst |
| By: | Akram, Qaisar Farooq; Rime, Dagfinn; Sarno, Lucio |
| Abstract: | This paper provides real-time evidence on the frequency, size, duration and economic significance of arbitrage opportunities in the foreign exchange market. We investigate deviations from the covered interest rate parity (CIP) condition using a unique data set for three major capital and foreign exchange markets that covers a period of more than seven months at tick frequency. The analysis unveils that: i) short-lived violations of CIP arise; ii) the size of CIP violations can be economically significant; iii) their duration is, on average, high enough to allow agents to exploit them, but low enough to explain why such opportunities have gone undetected in much previous research using data at lower frequency. |
| Keywords: | arbitrage; covered interest rate parity; exchange rates; foreign exchange microstructure |
| JEL: | F31 F41 G14 G15 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6878&r=mst |
| By: | Jean Jacod; Yingying Li; Per A. Mykland; Mark Podolskij; Mathias Vetter (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility – in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possess an intuitive transparency, can generate rate optimal estimators (with convergence rate n-1/4). |
| Keywords: | consistency, continuity, discrete observation, Itô process, leverage effect, pre-averaging, quarticity, realized volatility, stable convergence |
| JEL: | C10 C13 C14 |
| Date: | 2007–12–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-43&r=mst |
| By: | Thabo Mokoena (South African Reserve Bank, Pretoria); Rangan Gupta (Department of Economics, University of Pretoria); Renee Van Eyden (Department of Economics, University of Pretoria) |
| Abstract: | The market microstructure approach has been applied to the three major puzzles of exchange rate economics: the forward bias puzzle, the excess volatility puzzle, and the exchange rate determination puzzle. It claims that the imbalances between ‘buyer-initiated and seller-initiated trades’ in foreign exchange markets are indicative of the transmission link between exchange rates and fundamental determinants of exchange rates. In the context of the exchange rate determination puzzle, this paper discusses the market microstructure approach from the stand point of hybrid models that integrate order flow, fundamentals and non-fundamental variables to establish the determinants of the rand-dollar exchange rate. Among the non-fundamentals considered is the Economist commodity price index, the relevance of which is based on Chen and Rogoff (2002). Another non-fundamental variable included is a proxy for country risk—the differential between the Global Emerging Market Bond Index and the South African long-term bond. The paper relies on the autoregressive distributed lag (ARDL) model of Persaran, Shin and Smith (2001) and as explained in Persaran and Persaran (1997). The ARDL approach to cointegration does not require pre-testing for the integration properties of the individual series used in the empirical analysis. Instead, it relies on a bounds testing procedure. In this setting, inference is based on an F-test on the significance of lagged levels of variables in the error correction form. The results, based on the Schwarz Bayesian Criterion for choosing a model’s lag length, show that the there is a long-run relationship between the rand-dollar real exchange rate, nonfundamentals, the fundamentals and the proxy for order flow, which is the dollar-denominated daily net turnover on the South African markets. |
| Keywords: | Market Microstructure, Real Exchange Rates, ARDL |
| JEL: | C32 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:200810&r=mst |
| 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 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2007-16&r=mst |
| By: | John A Carlson; Christian M. Dahl; Carol L. Osler (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | Recent research has revealed a wealth of information about the microeconomics of currency markets and thus the determination of exchange rates at short horizons. This information is valuable to us as scientists since, like evidence of macroeconomic regularities, it can provide critical guidance for designing exchange-rate models. This paper presents an optimizing model of short-run exchange-rate dynamics consistent with both the micro evidence and the macro evidence, the first such model of which we are aware. With respect to microeconomics, the model is consistent with the institutional structure of currency markets, it accurately reflects the constraints and objectives faced by the major participants, and it fits key stylized facts concerning returns and order flow. With respect to macroeconomics, the model is consistent with most of the major puzzles that have emerged under floating rates. |
| Keywords: | Exchange-rate dynamics, currency market microstructure |
| JEL: | F31 G12 G15 |
| Date: | 2008–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-01&r=mst |
| By: | Michael Sørensen (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | A review is given of parametric estimation methods for discretely sampled mul- tivariate diffusion processes. The main focus is on estimating functions and asymp- totic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale estimating functions. Particular attention is given to explicit estimating functions. Results on both fixed frequency and high frequency asymptotics are given. When choosing among the many estima- tors available, guidance is provided by simple criteria for high frequency efficiency and rate optimality that are presented in the framework of approximate martingale estimating functions. |
| Keywords: | Asymptotic results, discrete time observation of a diffusion, efficiency, eigenfunctions, explicit inference, generalized method of moments, likelihood infer- ence, martingale estimating functions, high frequency asymptotics, Pearson diffu- sions. |
| JEL: | C22 C32 |
| Date: | 2008–04–04 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-18&r=mst |