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The continuous-time limit of score-driven volatility models

得分驱动波动率模型的连续时间极限

We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional second moment of the score, (iii) the normalization of the score. Interestingly, the properties of the stochastic differential…

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Diffusion copulas: Identification and estimation

扩散Copula:识别与估计

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations…

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Missing observations in observation-driven time series models

观测驱动时间序列模型中的缺失观测

We argue that existing methods for the treatment of missing observations in time-varying parameter observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for…

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Common pricing across asset classes: Empirical evidence revisited

跨资产类别的共同定价:重新审视经验证据

Intermediary and downside risk asset pricing theories lay the foundations for spanning the multi-asset return space by a small number of risk factors. Recent studies show strong empirical support for such factors across major asset classes. We revisit these results and show that robust evidence for common factor pricing remains elusive. Importantly, the proposed risk factors do not seem to provide incremental information to the traditional market factor. We argue that most…

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SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

期权观测误差中的空间依赖

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau…

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ExpectHill estimation, extreme risk and heavy tails

ExpectHill 估计、极端风险与重尾分布

Risk measures of a financial position are, from an empirical point of view, mainly based on quantiles. Replacing quantiles with their least squares analogues, called expectiles, has recently received increasing attention. The novel expectile-based risk measures satisfy all coherence requirements. We revisit their extreme value estimation for heavy-tailed distributions. First, we estimate the underlying tail index via weighted combinations of top order statistics and…

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Robust estimation of superhedging prices

超对冲价格的稳健估计

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with $d$ traded assets. We introduce a plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale…

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Estimation of a nonparametric model for bond prices from cross-section and time series information

结合横截面与时间序列信息的债券价格非参数估计

We develop a novel estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time…

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Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors

预测 VIX 与波动率风险溢价:短期融资利差波动因子的作用

This paper presents an innovative approach to extract Volatility Factors which predict the VIX, the S&P500 Realized Volatility (RV) and the Variance Risk Premium (VRP). The approach is innovative along two different dimensions, namely: (1) we extract Volatility Factors from panels of filtered volatilities — in particular large panels of univariate ARCH-type models and propose methods to estimate common Volatility Factors in the presence of estimation error and (2) we price…

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Real‐time detection of regimes of predictability in the US equity premium

美国股票风险溢价可预测状态的实时检测

Summary We propose new real‐time monitoring procedures for the emergence of end‐of‐sample predictive regimes using sequential implementations of standard (heteroskedasticity‐robust) regression t ‐statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in…

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When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility

移动平均模型与高频数据:波动率的一致有效推断

We conduct inference on volatility with noisy high‐frequency data. We assume the observed transaction price follows a continuous‐time Itô‐semimartingale, contaminated by a discrete‐time moving‐average noise process associated with the arrival of trades. We estimate volatility, defined as the quadratic variation of the semimartingale, by maximizing the likelihood of a misspecified moving‐average model, with its order selected based on an information criterion. Our inference…

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Fixed‐ k inference for volatility

波动率的固定k推断

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and…

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Average crossing time: An alternative characterization of mean aversion and reversion

平均穿越时间:均值远离与回归的另一种刻画

This study compares and contrasts the multiple characterizations of mean reversion in financial time series as regards the restrictions they imply. This is accomplished by translating them into statements about an alternative measure, the “Average Crossing Time” or ACT. We argue that the ACT measure, per se, provides not only a useful benchmark for the degree of mean reversion/aversion, but also an intuitive, and easily quantified sense of one time series being “more…

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Specification tests for non‐Gaussian maximum likelihood estimators

非高斯极大似然估计量的模型设定检验

We propose generalized DWH specification tests which simultaneously compare three or more likelihood‐based estimators in multivariate conditionally heteroskedastic dynamic regression models. Our tests are useful for Garch models and in many empirically relevant macro and finance applications involving Var s and multivariate regressions. We determine the rank of the differences between the estimators' asymptotic covariance matrices under correct specification, and take into…

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Inference for conditional value-at-risk of a predictive regression

预测回归中条件风险价值的统计推断

Conditional value-at-risk is a popular risk measure in risk management. We study the inference problem of conditional value-at-risk under a linear predictive regression model. We derive the asymptotic distribution of the least squares estimator for the conditional value-at-risk. Our results relax the model assumptions made in (Oper. Res. 60 (2012) 739–756) and correct their mistake in the asymptotic variance expression. We show that the asymptotic variance depends on the…

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High-frequency jump tests: Which test should we use?

高频跳跃检验:应选择哪一种检验?

We conduct an extensive evaluation of price jump tests based on high-frequency financial data. After providing a concise review of multiple alternative tests, we document the size and power of all tests in a range of empirically relevant scenarios. Particular focus is given to the robustness of test performance to the presence of jumps in volatility and microstructure noise, and to the impact of sampling frequency. The paper concludes by providing guidelines for empirical…

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High-dimensional predictive regression in the presence of cointegration

存在协整时的高维预测回归

We propose a Least Absolute Shrinkage and Selection Operator (LASSO) estimator of a predictive regression in which stock returns are conditioned on a large set of lagged covariates, some of which are highly persistent and potentially cointegrated. We establish the asymptotic properties of the proposed LASSO estimator and validate our theoretical findings using simulation studies. The application of this proposed LASSO approach to forecasting stock returns suggests that a…

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Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff

无限阶回归的非参数估计及其在风险收益权衡中的应用

This paper studies nonparametric estimation of the infinite order regression E(Ytk|Ft−1), k∈Z with stationary and weakly dependent data. We propose a Nadaraya–Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the issues of omitted information bias and specification error are…

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The term structure of equity and variance risk premia

股票与方差风险溢价的期限结构

We study the term structure of variance swaps, equity and variance risk premia. A model-free analysis reveals a significant price jump component in variance swaps. A model-based analysis shows that investors’ willingness to ensure against volatility risk increases after a market drop. This effect is stronger for short maturities, but more persistent for long maturities. During the financial crisis investors demanded large risk premia to hold equities, but the risk premia…

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Policy uncertainty and corporate credit spreads

政策不确定性与企业信用利差

We find a significant positive relation between changes in policy uncertainty and changes in credit spreads. Macroeconomic conditions, including general uncertainty, do not explain this result, which also holds when we use instrumental variables to address endogeneity issues. The impact of policy uncertainty is greater for firms that operate in regulation-intensive industries, face high tax rates, or are dependent on government spending. It is also stronger for firms that…

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TESTING FOR STRUCTURAL CHANGES IN FACTOR MODELS VIA A NONPARAMETRIC REGRESSION

通过非参数回归检验因子模型的结构变化

We propose a model-free test for structural changes in factor models. The basic idea is to regress the data on commonly estimated factors by local smoothing and compare the fitted values of time-varying factor loadings with those of time-invariant factor loadings estimated via principal component analysis. By construction, the test is designed to be powerful against both smooth structural changes and sudden structural breaks with a possibly unknown number of breaks and…

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Estimation and inference of change points in high-dimensional factor models

高维因子模型中变点的估计与推断

In this paper, we consider the estimation of break points in high-dimensional factor models where the unobserved factors are estimated by principal component analysis (PCA). The factor loading matrix is assumed to have a structural break at an unknown time. We establish the conditions under which the least squares (LS) estimator is consistent for the break date. Our consistency result holds for both large and small breaks. We also find the LS estimator’s asymptotic…

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The term structure and inflation uncertainty

利率期限结构与通胀不确定性

To assess the importance of inflation risk for nominal Treasury yields, a novel quadratic term structure model with time-varying inflation risk is estimated using survey-based inflation uncertainty. The resulting yield decomposition captures very diverse macroeconomic dynamics of inflation and real risk premiums (large and positive during the 1980s but small and negative post-2008) and generates sensible high-frequency estimates of expected inflation and real short rates…

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The Five Trolls Under the Bridge: Principal Component Analysis With Asynchronous and Noisy High Frequency Data

桥下的五个巨魔:异步且含噪高频数据的主成分分析

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of the spot covariance matrix is developed based on the smoothed two-scale realized variance (S-TSRV). The fourth troll is how to pass from estimated time-varying covariance…

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