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一致最小方差无偏分块估计量AI 解读

We provide necessary and sufficient conditions for an (Unbiased) Block estimator to have Uniformly Minimum Variance. Our theory parallels the theory of UMVU estimation, the main novel insight being the focus on the covariance among blocks. We use this theory to derive lower variance bounds for block estimators of functionals of high-frequency volatility when the block size is fixed. We further show the relevance of the new theory for the classical problem of estimation of…

已实现漂移AI 解读

Drift and volatility are two mainsprings of asset price dynamics. While volatilities have been studied extensively in the literature, drifts are commonly believed to be impossible to estimate and largely ignored in the literature. This paper shows how to detect drift using realized autocovariance implemented on high-frequency data. We use a theoretical treatment in which the classical model for the efficient price, an Itō semimartingale possibly contaminated by…

利用有偏代理变量评估预测表现AI 解读

This paper rehabilitates biased proxies for the assessment of the predictive accuracy of competing forecasts. By relaxing the ubiquitous assumption of proxy unbiasedness adopted in the theoretical and empirical literature, we show how to optimally combine (possibly) biased proxies to maximize the probability of inferring the ranking that would be obtained using the true latent variable, a property that we dub proxy reliability. Our procedure still preserves the robustness of…

价格跳跃还是价格停滞？AI 解读

Even moderate amounts of zero returns in financial data, associated with stale prices, are heavily detrimental for reliable jump inference. We harness staleness-robust estimators to reappraise the statistical features of jumps in financial markets. We find that jumps are much less frequent and much less contributing to price variation than what found by the empirical literature so far. In particular, the empirical finding that volatility is driven by a pure jump process is…

系统性价格停滞AI 解读

Asset prices are stale. We define a measure of systematic (market-wide) staleness as the percentage of small price adjustments across multiple assets. A notion of idiosyncratic (asset-specific) staleness is also established. For both systematic and idiosyncratic staleness, we provide a limit theory based on joint asymptotics relying on increasingly-frequent observations over a fixed time span and an increasing number of assets. Using systematic and idiosyncratic staleness as…

漂移突增假说AI 解读

The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms of liquidity provision. We show how to build drift bursts into the…

尾部中的 BetaAI 解读

Do hedge funds hedge? In negative states of the world, often not as much as they should. For several styles, we report larger market betas when market returns are low (i.e., “beta in the tails”). We justify this finding through a combination of negative-mean jumps in the market returns and large market jump betas: when moving to the left tail of the market return distribution jump dynamics dominate continuous dynamics and the overall systematic risk of the fund is driven by…

非参数随机波动率建模AI 解读

We provide nonparametric methods for stochastic volatility modeling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, and jumps in returns and volatility with possibly state-dependent jump intensities, among other features. In the first stage, we identify spot volatility by virtue of jump-robust nonparametric estimates. Using observed prices and estimated spot volatilities,…

时变杠杆效应AI 解读

Vast empirical evidence points to the existence of a negative correlation, named ”leverage effect”, between shocks to variance and shocks to returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in returns, jumps in variance, or both. Leverage is defined as a flexible function of the state of the firm, as summarized by the spot variance level. We show that its point-wise functional…

具有持续性杠杆效应的离散时间波动率预测及其与连续时间建模的联系AI 解读

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models that are able to reproduce the…

带跳跃马尔可夫模型的阈值估计与利率建模AI 解读

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in the presence of both finite and infinite activity (finite variation) jumps. Our results rely on kernel estimation, using the properties of the local time of the data generating process, and the fact that it is possible to disentangle the discontinuous part of the state…

阈值双幂变差与跳跃对波动率预测的影响AI 解读

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent, but also scarcely plagued by small sample bias. With the aim of achieving this, we introduce the concept of threshold bipower variation, which is based on the joint…

随机波动模型扩散系数的非参数估计AI 解读

In this paper, new fully nonparametric estimators of the diffusion coefficient of continuous time models are introduced. The estimators are based on Fourier analysis of the state variable trajectory observed and on the estimation of quadratic variation between observations by means of realized volatility. The estimators proposed are shown to be consistent and asymptotically normally distributed. Moreover, the Fourier estimator can be iterated to get a fully nonparametric…