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混合时间尺度跳跃回归与自助法推断AI 解读

We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard…

利用高频数据自适应估计连续时间回归模型AI 解读

We derive the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous-time regression model for the continuous martingale parts of two Itô semimartingales observed on a fixed time interval with asymptotically shrinking mesh of the observation grid. We further construct an estimator from high-frequency data that achieves this efficiency bound and, indeed, is adaptive to the presence of infinite-dimensional nuisance components. The…

In this paper, we propose a test for deciding whether the jump activity index of a discretely observed Itô semimartingale of pure-jump type (i.e., one without a diffusion) varies over a fixed interval of time. The asymptotic setting is based on observations within a fixed time interval with mesh of the observation grid shrinking to zero. The test is derived for semimartingales whose “spot” jump compensator around zero is like that of a stable process, but importantly the…

稳健跳跃回归AI 解读

We develop robust inference methods for studying linear dependence between the jumps of discretely observed processes at high frequency. Unlike classical linear regressions, jump regressions are determined by a small number of jumps occurring over a fixed time interval and the rest of the components of the processes around the jump times. The latter are the continuous martingale parts of the processes as well as observation noise. By sampling more frequently the role of…

跳跃回归AI 解读

We develop econometric tools for studying jump dependence of two processes from high‐frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference. We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We…

通过正则化拉普拉斯反演估计波动率占用时间AI 解读

We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in…

波动率函数依赖关系的推断理论AI 解读

We develop inference theory for models involving possibly nonlinear transforms of the elements of the spot covariance matrix of a multivariate continuous-time process observed at high frequency. The framework can be used to study the relationship among the elements of the latent spot covariance matrix and processes defined on the basis of it such as systematic and idiosyncratic variances, factor betas and correlations on a fixed interval of time. The estimation is based on…

指数期权中蕴含的风险溢价AI 解读

We study the dynamic relation between market risks and risk premia using time series of index option surfaces. We find that priced left tail risk cannot be spanned by market volatility (and its components) and introduce a new tail factor. This tail factor has no incremental predictive power for future volatility and jump risks, beyond current and past volatility, but is critical in predicting future market equity and variance risk premia. Our findings suggest a wide wedge…

利用自归一化统计量估计纯跳半鞅的跳跃活跃度AI 解读

We derive a nonparametric estimator of the jump-activity index $\beta$ of a “locally-stable” pure-jump Itô semimartingale from discrete observations of the process on a fixed time interval with mesh of the observation grid shrinking to zero. The estimator is based on the empirical characteristic function of the increments of the process scaled by local power variations formed from blocks of increments spanning shrinking time intervals preceding the increments to be scaled.…

基于期权面板的参数推断与动态状态恢复AI 解读

We develop a new parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for…

时变跳跃尾部AI 解读

We develop new methods for the estimation of time-varying risk-neutral jump tails in asset returns. In contrast to existing procedures based on tightly parameterized models, our approach imposes much fewer structural assumptions, relying on extreme-value theory approximations together with short-maturity options. The new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ, and importantly for the tail shape…

存在无限变差跳跃时积分波动率的有效估计AI 解读

We propose new nonparametric estimators of the integrated volatility of an Itô semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the optimal rate and variance of estimating integrated volatility even in the presence of infinite variation jumps when the latter are stochastic integrals with respect to locally “stable” Lévy processes, that is, processes whose Lévy measure…

波动率活动度：模型设定与估计AI 解读

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high-frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods for estimating and evaluating, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX…

波动率占用时间AI 解读

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a…

跳跃扩散中以逆已实现拉普拉斯变换估计波动率密度AI 解读

This article develops a nonparametric estimator of the stochastic volatility density of a discretely observed Itô semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two basic steps involved. The first step is aggregating the high-frequency increments into the realized Laplace transform, which is a robust nonparametric estimate of the underlying volatility Laplace transform. The second step is using a regularized kernel…

纯跳半鞅的已实现拉普拉斯变换AI 解读

We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Lévy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed…

用于跳跃扩散波动率模型估计的已实现拉普拉斯变换AI 解读

We develop an efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model-free estimate of the daily integrated empirical Laplace transform of the unobservable volatility. The estimation is then done by matching moments of the integrated joint Laplace transform with those implied by the…

波动率跳跃AI 解读

The article undertakes a nonparametric analysis of the high-frequency movements in stock market volatility using very finely sampled data on the VIX volatility index compiled from options data by the CBOE. We derive theoretically the link between pathwise properties of the latent spot volatility and the VIX index, such as presence of continuous martingale and/or jumps, and further show how to make statistical inference about them from the observed data. Our empirical results…

跳跃驱动随机波动率模型的计量分析AI 解读

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first, the price has a continuous component with time-varying volatility and time-homogeneous jumps. The second jump-driven stochastic volatility model…

跳跃与贝塔：系统性风险的分离和估计AI 解读

We provide a new theoretical framework for disentangling and estimating the sensitivity towards systematic diffusive and jump risks in the context of factor 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. We show consistency and derive the asymptotic distributions of our estimators. In an empirical application of the new procedures involving high-frequency…

高频数据分析的活动特征函数AI 解读

We define a new concept termed activity signature function, which is constructed from discrete observations of a continuous-time process, and derive its asymptotic properties as the sampling frequency increases. We show that the function is a useful device for estimating the activity level of the underlying process and in particular for deciding whether the process contains a continuous martingale. An application to $ /DM exchange rate over 1986-1999 indicates that a…

离散观测多维过程的共同跳跃检验AI 解读

We consider a bivariate process Xt=(Xt1, Xt2), which is observed on a finite time interval [0, T] at discrete times 0, Δn, 2Δn, …. Assuming that its two components X1 and X2 have jumps on [0, T], we derive tests to decide whether they have at least one jump occurring at the same time (“common jumps”) or not (“disjoint jumps”). There are two different tests for the two possible null hypotheses (common jumps or disjoint jumps). Those tests have a prescribed asymptotic level,…

利用高频数据估计含跳跃的连续时间随机波动率模型AI 解读

This paper proposes a method of inference for general stochastic volatility models containing price jumps. The estimation is based on treating realized multipower variation statistics calculated from high-frequency data as their unobservable (fill-in) asymptotic limits. The paper provides easy-to-check conditions under which the error in estimation resulting from this approximation is op(1) and additional ones under which it is , where T is the number of days in the sample.…

Lévy 驱动的连续时间 CARMA 随机波动率模型模拟方法AI 解读

We develop simulation schemes for the new classes of non-Gaussian pure jump Lévy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Lévy process, which makes series approximation methods directly applicable. These methods entail simulation of the Lévy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function or specification of a copula…