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Identifying the volatility risk price through the leverage effect

通过杠杆效应识别波动率风险价格

In asset pricing models with stochastic volatility, uncertainty about volatility affects risk premia through two channels: aversion to decreasing returns and aversion to increasing volatility. We analyze the identification of and robust inference for structural parameters measuring investors’ aversions to these risks: the return risk price and the volatility risk price. In the presence of a leverage effect (instantaneous causality between the asset return and its…

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IN-SAMPLE ASYMPTOTICS AND ACROSS-SAMPLE EFFICIENCY GAINS FOR HIGH FREQUENCY DATA STATISTICS

高频统计量的样本内渐近分析与跨样本效率增益

We revisit in-sample asymptotic analysis extensively used in the realized volatility literature. We show that there are gains to be made in estimating current realized volatility from considering realizations in prior periods. The weighting schemes also relate to Kalman-Bucy filters, although our approach is non-Gaussian and model-free. We derive theoretical results for a broad class of processes pertaining to volatility, higher moments, and leverage. The paper also contains…

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The leverage effect puzzle revisited: Identification in discrete time

重新审视杠杆效应之谜:离散时间中的识别

The term “leverage effect,” as coined by Black (1976), refers to the tendency of an asset’s volatility to be negatively correlated with the asset’s return. Aït-Sahalia et al. (2013) refer to the “leverage effect puzzle” as the fact that, in spite of a broad agreement that the effect should be present, it is hard to identify empirically. For this purpose, we propose an extension with leverage effect of the discrete time stochastic volatility model of Darolles et al. (2006).…

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Identifying contagion

识别金融传染

Summary Identifying contagion effects during periods of financial crisis is known to be complicated by the changing volatility of asset returns during periods of stress. To untangle this we propose a GARCH (generalized autoregressive conditional heteroskedasticity) common features approach, where systemic risk emerges from a common factor source (or indeed multiple factor sources) with contagion evident through possible changes in the factor loadings relating to the common…

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Efficient two-step estimation via targeting

通过目标化实现高效两步估计

The standard description of two-step extremum estimation amounts to plugging-in a first-step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly, but potentially inefficient, estimator for the parameters of interest. In this paper, we consider a more general setting of two-step estimation where we do not necessarily have ‘nuisance parameters’ but rather awkward occurrences of the parameters of interest. The efficiency…

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EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY AND RELATED PROCESSES

积分波动率及相关过程的有效估计

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds,…

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Maximization by parts in extremum estimation

极值估计中的分部极大化

In this paper, we present various iterative algorithms for extremum estimation in cases where direct computation of the extremum estimator or via the Newton–Raphson algorithm is difficult, if not impossible. While the Newton–Raphson algorithm makes use of the full Hessian matrix, which may be difficult to evaluate, our algorithms use parts of the Hessian matrix only, the parts that are easier to compute. We establish consistency and asymptotic efficiency of our iterative…

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REALIZED VOLATILITY WHEN SAMPLING TIMES ARE POSSIBLY ENDOGENOUS

采样时点可能内生时的已实现波动率

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the realized volatility in a general endogenous time setting. We also establish a central limit theorem for the tricity under the hypothesis that there is no endogeneity, based on which we propose a test and document that this…

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Causality effects in return volatility measures with random times

随机时间下收益波动率度量中的因果效应

We provide a structural approach to identify instantaneous causality effects between durations and stock price volatility. So far, in the literature, instantaneous causality effects have either been excluded or cannot be identified separately from Granger type causality effects. By giving explicit moment conditions for observed returns over (random) duration intervals, we are able to identify an instantaneous causality effect. The documented causality effect has significant…

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Statistical Inference for Random-Variance Option Pricing

随机方差期权定价的统计推断

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based on the different information sets. Both approaches are based on indirect inference and avoid any discretization bias by simulating the continuous-time model. We assume an…

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