Haipeng Xing

Modeling high-frequency volatility is an important topic of market microstructure, as it provides the empirical tools to measure and analyze the rapid price movements. Yet, volatility at a high frequency often exhibits abrupt shifts driven by news and trading activity, making accurate estimation challenging. This study develops a change-point duration (CPD) model to estimate spot volatility, in which price-change intensities remain constant between events but may shift at random change points. Using simulations and empirical analysis of Nasdaq limit order book data, we demonstrate that the CPD model achieves a favorable balance between responsiveness to sudden shocks and stability in volatility dynamics. Moreover, it outperforms benchmark approaches, including the classical autoregressive conditional duration model, nonparametric duration-based estimators, and candlestick-based measures. These findings highlight the CPD framework as an effective tool for volatility estimation in high-frequency trading environments.

The complexity of estimating multivariate GARCH models increases significantly with the increase in the number of asset series. To address this issue, we propose a general regularization framework for high-dimensional GARCH models with BEKK representations, and obtain a penalized quasi-maximum likelihood (PQML) estimator. Under some regularity conditions, we establish some theoretical properties, such as the sparsity and the consistency, of the PQML estimator for the BEKK representations. We then carry out simulation studies to show the performance of the proposed inference framework and the procedure for selecting tuning parameters. In addition, we apply the proposed framework to analyze volatility spillover and portfolio optimization problems, using daily prices of 18 U.S. stocks from January 2016 to January 2018, and show that the proposed framework outperforms some benchmark models.

This paper extends Xing's (2023abcd) optimal growth models of catching-up economies from the case of production function switching to that of economic structure switching and argues how a country develops its economy by endogenous structural transformation and efficient resource allocation in a market mechanism. To achieve this goal, the paper first summarizes three attributes of economic structures from the literature, namely, structurality, durationality, and transformality, and discuss their implications for methods of economic modeling. Then, with the common knowledge assumption, the paper extends Xing's (2023a) optimal growth model that is based on production function switching and considers an extended Ramsey model with endogenous structural transformation in which the social planner chooses the optimal industrial structure, recource allocation with the chosen structure, and consumption to maximize the representative household's total utility subject to the resource constraint. The paper next establishes the mathematical underpinning of the static, dynamic, and switching equilibria. The Ramsey growth model and its equilibria are then extended to economies with complicated economic structures consisting of hierarchical production, technology adoption and innovation, infrastructure, and economic and political institutions. The paper concludes with a brief discussion of applications of the proposed methodology to economic development problems in other scenarios.

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies that determine optimally both trade times and number of shares in a pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem that involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.

Quote volatility is important in determining the cost of demand in a high frequency (HF) order market. This paper proposes a new model to measure quote volatility based on the point process and price-change duration. Specifically, we built a change-point intensity (CPI) model to describe the dynamics of price-change events for a given level of threshold. The instantaneous volatility of quote price can be calculated at any time according to price-change intensities. Based on this, we can quantify the cost of demanding liquidity for traders with different trading latency by using integrated variances. Furthermore, we use the autoregressive conditional intensity (ACI) model proposed by Russell (1999) as a benchmark comparison. The results suggest that our model has better performance of both in-sample fitness and out-of-sample prediction.

The B cells in our body generate protective antibodies by introducing somatic hypermutations (SHM) into the variable region of immunoglobulin genes (IgVs). The mutations are generated by activation induced deaminase (AID) that converts cytosine to uracil in single stranded DNA (ssDNA) generated during transcription. Attempts have been made to correlate SHM with ssDNA using bisulfite to chemically convert cytosines that are accessible in the intact chromatin of mutating B cells. These studies have been complicated by using different definitions of “bisulfite accessible regions” (BARs). Recently, deep-sequencing has provided much larger datasets of such regions but computational methods are needed to enable this analysis. Here we leveraged the deep-sequencing approach with unique molecular identifiers and developed a novel Hidden Markov Model based Bayesian Segmentation algorithm to characterize the ssDNA regions in the IGHV4-34 gene of the human Ramos B cell line. Combining hierarchical clustering and our new Bayesian model, we identified recurrent BARs in certain subregions of both top and bottom strands of this gene. Using this new system, the average size of BARs is about 15 bp. We also identified potential G-quadruplex DNA structures in this gene and found that the BARs co-locate with G-quadruplex structures in the opposite strand. Using various correlation analyses, there is not a direct site-to-site relationship between the bisulfite accessible ssDNA and all sites of SHM but most of the highly AID mutated sites are within 15 bp of a BAR. In summary, we developed a novel platform to study single stranded DNA in chromatin at a base pair resolution that reveals potential relationships among BARs, SHM and G-quadruplexes. This platform could be applied to genome wide studies in the future.

Background: The nucleus of eukaryotic cells spatially packages chromosomes into a hierarchical and distinct segregation that plays critical roles in maintaining transcription regulation. High-throughput methods of chromosome conformation capture, such as Hi-C, have revealed topologically associating domains (TADs) that are defined by biased chromatin interactions within them.Results: We introduce a novel method, HiCKey, to decipher hierarchical TAD structures in Hi-C data and compare them across samples. We first derive a generalized likelihood-ratio (GLR) test for detecting change-points in an interaction matrix that follows a negative binomial distribution or general mixture distribution. We then employ several optimal search strategies to decipher hierarchical TADs withpvalues calculated by the GLR test. Large-scale validations of simulation data show that HiCKey has good precision in recalling known TADs and is robust against random collisions of chromatin interactions. By applying HiCKey to Hi-C data of seven human cell lines, we identified multiple layers of TAD organization among them, but the vast majority had no more than four layers. In particular, we found that TAD boundaries are significantly enriched in active chromosomal regions compared to repressed regions.Conclusions: HiCKey is optimized for processing large matrices constructed from high-resolution Hi-C experiments. The method and theoretical result of the GLR test provide a general framework for significance testing of similar experimental chromatin interaction data that may not fully follow negative binomial distributions but rather more general mixture distributions.

The 2007–2008 financial crisis had severe consequences on the global economy and an intriguing question related to the crisis is whether structural breaks in the credit market can be detected. To address this issue, we chose firms’ credit rating transition dynamics as a proxy of the credit market and discuss how statistical process control tools can be used to surveil structural breaks in firms’ rating transition dynamics. After reviewing some commonly used Markovian models for firms’ rating transition dynamics, we present several surveillance rules for detecting changes in generators of firms’ rating migration matrices, including the likelihood ratio rule, the generalized likelihood ratio rule, the extended Shiryaev’s detection rule, and a Bayesian detection rule for piecewise homogeneous Markovian models. The effectiveness of these rules was analyzed on the basis of Monte Carlo simulations. We also provide a real example that used the surveillance rules to analyze and detect structural breaks in the monthly credit rating migration of U.S. firms from January 1986 to February 2017.

This paper studies inter-trade durations in the NASDAQ limit order market and finds that inter-trade durations in ultra-high frequency have two modes. One mode is to the order of approximately 10^{-4} seconds, and the other is to the order of 1 second. This phenomenon and other empirical evidence suggest that there are two regimes associated with the dynamics of inter-trade durations, and the regime switchings are driven by the changes of high-frequency traders (HFTs) between providing and taking liquidity. To find how the two modes depend on information in the limit order book (LOB), we propose a two-state multifactor regime-switching (MF-RSD) model for inter-trade durations, in which the probabilities transition matrices are time-varying and depend on some lagged LOB factors. The MF-RSD model has good in-sample fitness and the superior out-of-sample performance, compared with some benchmark duration models. Our findings of the effects of LOB factors on the inter-trade durations help to understand more about the high-frequency market microstructure.

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and number of shares in pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem which involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.