# Research articles for the 2021-01-05

arXiv

Traders constantly consider the price impact associated with changing their positions. This paper seeks to understand how price impact emerges from the quoting strategies of market makers. To this end, market making is modeled as a dynamic auction using the mathematical framework of Stochastic Differential Games. In Nash Equilibrium, the market makers' quoting strategies generate a price impact function that is of the same form as the celebrated Almgren-Chriss model. The key insight is that price impact is the mechanism through which market makers earn profits while matching their books. As such, price impact is an essential feature of markets where flow is intermediated by market makers.

arXiv

Sparse and short news headlines can be arbitrary, noisy, and ambiguous, making it difficult for classic topic model LDA designed for accommodating long text to discover knowledge from them. Nonetheless, some of the existing research about text-based crude oil forecasting employs LDA to explore topics from news headlines, resulting in a mismatch between the short text and the topic model and further affecting the forecasting performance. Exploiting advanced and appropriate methods to construct high-quality features from news headlines becomes crucial in crude oil forecasting. To tackle this issue, this paper introduces two novel indicators of topic and sentiment for the short and sparse text data. Empirical experiments show that AdaBoost.RT with our proposed text indicators, with a more comprehensive view and characterization of the short and sparse text data, outperforms the other benchmarks. Another significant merit is that our method also yields good forecasting performance when applied to other futures commodities.

arXiv

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized facts often found in volatility data. Our prime model is based on the so-called Brownian semistationary process and we derive a number of theoretical properties of this process, relevant to volatility modeling. Applying the models to realized volatility measures covering a vast panel of assets, we find evidence consistent with the hypothesis that time series of realized measures of volatility are both rough and very persistent. Lastly, we illustrate the utility of the models in an extensive forecasting study; we find that the models proposed in this paper outperform a wide array of benchmarks considerably, indicating that it pays off to exploit both roughness and persistence in volatility forecasting.

arXiv

We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations. We prove a Central Limit Theorem for the estimation error with an optimal rate and study the optimal selection of the bandwidth and kernel functions. We show that the pre-averaging/kernel estimator's asymptotic variance is minimal for exponential kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work. We also develop a feasible implementation of the proposed estimators with optimal bandwidth. Monte Carlo experiments confirm the superior performance of the devised method.

arXiv

We propose methods for constructing regularized mixtures of density forecasts. We explore a variety of objectives and regularization penalties, and we use them in a substantive exploration of Eurozone inflation and real interest rate density forecasts. All individual inflation forecasters (even the ex post best forecaster) are outperformed by our regularized mixtures. From the Great Recession onward, the optimal regularization tends to move density forecasts' probability mass from the centers to the tails, correcting for overconfidence.

arXiv

We consider a futures hedging problem subject to a budget constraint that limits the ability of a hedger with default aversion to meet margin requirements. We derive a semi-closed form for an optimal hedging strategy with dual objectives -- to minimize both the variance of the hedged portfolio and the probability of forced liquidations due to margin calls. An empirical analysis of bitcoin shows that the optimal strategy not only achieves superior hedge effectiveness, but also reduces the probability of forced liquidations to an acceptable level. We also compare how the hedger's default aversion impacts the performance of optimal hedging based on minute-level data across major bitcoin spot and perpetual futures markets.

arXiv

Predicting Residential Property Value in Catonsville, Maryland: A Comparison of Multiple Regression Techniques

arXiv

Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural networks-based algorithms to solve stochastic control problems with delay features. Specifically, we employ neural networks for sequence modeling (\emph{e.g.}, recurrent neural networks such as long short-term memory) to parameterize the policy and optimize the objective function. The proposed algorithms are tested on three benchmark examples: a linear-quadratic problem, optimal consumption with fixed finite delay, and portfolio optimization with complete memory. Particularly, we notice that the architecture of recurrent neural networks naturally captures the path-dependent feature with much flexibility and yields better performance with more efficient and stable training of the network compared to feedforward networks. The superiority is even evident in the case of portfolio optimization with complete memory, which features infinite delay.

arXiv

Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association. These bounds have been computed for Spearman's rho, Kendall's tau, and Blomqvist's beta. The importance of another two measures of association, Spearman's footrule and Gini's gamma, has been reconfirmed recently. It is the main purpose of this paper to fill in the gap and present the mentioned local bounds for these two measures as well. It turns out that this is a quite non-trivial endeavor as the bounds are quasi-copulas that are not copulas for certain values of the two measures. We also give relations between these two measures of association and Blomqvist's beta.