每日简报

波动率恒定性的尖锐自适应非参数检验AI 解读

Based on discrete observations, we develop a test to infer if the volatility function $σ(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = σ(t)dW_t$ is constant. The testing procedure is shown to be minimax-optimal and adaptive for infill asymptotics and these results entail that a deviation from the null hypothesis of constancy is best measured in terms of the ratio of $σ(t)$ and its $L^2$-average. The derivation of optimal constants requires the…

GARCH-X 模型的一致变量选择AI 解读

In this paper we develop a consistent variable selection procedure for GARCH-X models that identifies the truly relevant exogenous covariates influencing volatility dynamics. The proposed method is based on a multiple hypothesis testing framework with Wald-type test statistics and the Benjamini-Yekutieli False Discovery Rate (FDR) procedure to control the proportion of false discoveries. We establish the consistency of the selection rule, showing that it asymptotically…

ARCH-m(X) 模型的非参数检验与变量选择AI 解读

We introduce the ARCH-m(X) model, a semiparametric extension of the ARCH-X framework in which the effect of a multivariate exogenous covariate vector X on the conditional variance is modeled through an unknown nonparametric function m(), accommodating complex nonlinear relationships between external predictors and financial volatility. Within this model, we develop a novel hypothesis test for the significance of covariates constructed with an artificial one-way ANOVA. Under…

检测显著预测变量的高维 Wild Bootstrap 最大值检验AI 解读

We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be screened may be large $p$ $>>$ $n$, and growing at an exponential rate, provided $\ln (p)$ $=$ $o(n^{a})$ for some $a$ $>$ $0$ that depends on memory decay and the growth of higher moments. We study the problem of correlation screening in a…

利用二元 Gamma 广义 Laplace 分布建模股票收益与波动率AI 解读

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case,…

通过课程学习与耦合 PINN 为 Heston 模型下的美式期权定价AI 解读

In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an unknown, time-varying exercise boundary. The Heston model is one of the most popular ways to model real market behavior because it allows volatility to change over time. However, unlike European options, there is no closed-form solution…

高斯—柯西卷积模型的精确似然推断与稳健滤波AI 解读

The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, Fisher information, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt…

基于瞬时波动率的四次变差估计札记AI 解读

We study an estimator of twice the integrated quarticity of a continuous Itô semimartingale, constructed from squared returns and local estimates of spot volatility. For a shrinking estimation window, we establish a functional stable central limit theorem for a bias-corrected version of the estimator. The limiting conditional variance is $56\int_0^t c_s^4\dd s$, where $c$ denotes spot variance. The proof identifies a common martingale approximation for the three components…

基于高频蜡烛图的瞬时回归AI 解读

Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks, extending conventional (open-to-close) returns with intra-period high/low prices. Specifically, I construct candlestick-based estimators of regression parameters, including spot beta, by minimizing a quadratic risk under a fixed-k asymptotic…

波动率粗糙度的随机化 Kolmogorov–Smirnov 分析AI 解读

We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the temporal dependence of financial volatility, we propose a random permutation procedure that effectively removes serial correlation while preserving marginal distributions, enabling the rigorous application of the KS framework to dependent…