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139
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
Abstract

Cited by 268 (34 self)
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this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionallyintegrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated highfrequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormalnormal mixture forecast distribution provides conditionally wellcalibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitragefree multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from highfrequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
The Distribution of Realized Exchange Rate Volatility
 Journal of the American Statistical Association
, 2001
"... Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately ..."
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Cited by 155 (18 self)
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Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.
Solving ForwardBackward Stochastic Differential Equations Explicitly – a Four Step Scheme
 Prob. Th. Rel. Fields
, 1994
"... Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability ..."
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Cited by 88 (11 self)
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Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and su cient condition for the solvability of the linear FBSDEs with the processes Z (serves as a correction, see x1) being absent in the drift. Then a Riccati type equation for matrixvalued (not necessarily square) functions is derived using the idea of the FourStepScheme (introduced in [11] for general FBSDEs). The solvability of such a Riccati type equation is studied which leads to a representation of adapted solutions to linear FBSDEs. Keywords. Linear forwardbackward stochastic di erential equations, adapted solution, Riccati type equation. AMS Mathematics subject classi cation. 60H10.
New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model
 Journal of Business
, 1998
"... We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black ..."
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Cited by 79 (7 self)
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We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical BlackScholes model. We study implicit volatilities, the smile effect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit riskneutral density function from option data. Finally we present some new valueat risk calculations leading to new perspectives to cope with model risk. I Introduction There is little doubt that the BlackScholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...
Functional Limit Theorems For Multitype Branching Processes And Generalized Pólya Urns
 APPL
, 2004
"... A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for example when the total number of particles reaches a given level. Using the ..."
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Cited by 64 (13 self)
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A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for example when the total number of particles reaches a given level. Using the
Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility
, 2000
"... We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which ..."
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Cited by 53 (7 self)
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We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which is effectively approximated by the quadratic variation of the process. We successfully implement the resulting GMM estimator with highfrequency fiveminute foreign exchange and equity index returns. Our simulation evidence and actual empirical results indicate that the method is very reliable and accurate. The computational speed of the procedure compares very favorably to other existing estimation methods in the literature.
The effects of random and discrete sampling when estimating continuoustime diffusions
 ECONOMETRICA
, 2003
"... Highfrequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuoustime model. In particular, we measure the additional effects of the randomn ..."
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Cited by 48 (10 self)
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Highfrequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuoustime model. In particular, we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data. We also examine the effect of simply ignoring the sampling randomness. We find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data.
2003), “Correcting the Errors: Volatility Forecast Evaluation Using HighFrequency Data and Realized Volatilities,” working paper
"... We develop general modelfree adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent nonparametric asymptotic distributional results in BarndorffNielsen and Shephard (200 ..."
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Cited by 41 (11 self)
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We develop general modelfree adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent nonparametric asymptotic distributional results in BarndorffNielsen and Shephard (2002a) along with new results explicitly allowing for leverage effects, are both easytoimplement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return volatility predictability.
Jumps in financial markets: A new nonparametric test and jump clustering
, 2007
"... This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dyn ..."
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Cited by 39 (2 self)
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This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dynamics and their distributions in the U.S. equity markets. The results show that individual stock jumps are associated with prescheduled earnings announcements and other companyspecific news events. Additionally, S&P 500 Index jumps are associated with general market news announcements. This suggests different pricing models for individual equity options versus index options. (JEL G12, G22, G14) Financial markets sometimes generate significant discontinuities, socalled jumps, in financial variables. A number of recent empirical and theoretical studies proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing