High-Frequency Data

Student t-Lévy regression model in YUIMA ArXiv ID: 2403.12078 “View on arXiv” Authors: Unknown Abstract The aim of this paper is to discuss an estimation and a simulation method in the \textsf{“R”} package YUIMA for a linear regression model driven by a Student-$t$ Lévy process with constant scale and arbitrary degrees of freedom. This process finds applications in several fields, for example finance, physic, biology, etc. The model presents two main issues. The first is related to the simulation of a sample path at high-frequency level. Indeed, only the $t$-Lévy increments defined on an unitary time interval are Student-$t$ distributed. In YUIMA, we solve this problem by means of the inverse Fourier transform for simulating the increments of a Student-$t$ Lévy defined on a interval with any length. A second problem is due to the fact that joint estimation of trend, scale, and degrees of freedom does not seem to have been investigated as yet. In YUIMA, we develop a two-step estimation procedure that efficiently deals with this issue. Numerical examples are given in order to explain methods and classes used in the YUIMA package. ...

Robust Estimation of Realized Correlation: New Insight about Intraday Fluctuations in Market Betas ArXiv ID: 2310.19992 “View on arXiv” Authors: Unknown Abstract Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel subsampled quadrant estimator that improves efficiency while preserving consistency and robustness. This estimator is particularly well-suited for high-frequency financial data and we apply it to a large panel of US stocks. Our empirical analysis sheds new light on intra-day fluctuations in market betas by decomposing them into time-varying correlations and relative volatility changes. Our results show that intraday variation in betas is primarily driven by intraday variation in correlations. ...

Transformers versus LSTMs for electronic trading ArXiv ID: 2309.11400 “View on arXiv” Authors: Unknown Abstract With the rapid development of artificial intelligence, long short term memory (LSTM), one kind of recurrent neural network (RNN), has been widely applied in time series prediction. Like RNN, Transformer is designed to handle the sequential data. As Transformer achieved great success in Natural Language Processing (NLP), researchers got interested in Transformer’s performance on time series prediction, and plenty of Transformer-based solutions on long time series forecasting have come out recently. However, when it comes to financial time series prediction, LSTM is still a dominant architecture. Therefore, the question this study wants to answer is: whether the Transformer-based model can be applied in financial time series prediction and beat LSTM. To answer this question, various LSTM-based and Transformer-based models are compared on multiple financial prediction tasks based on high-frequency limit order book data. A new LSTM-based model called DLSTM is built and new architecture for the Transformer-based model is designed to adapt for financial prediction. The experiment result reflects that the Transformer-based model only has the limited advantage in absolute price sequence prediction. The LSTM-based models show better and more robust performance on difference sequence prediction, such as price difference and price movement. ...

Real-time VaR Calculations for Crypto Derivatives in kdb+/q ArXiv ID: 2309.06393 “View on arXiv” Authors: Unknown Abstract Cryptocurrency market is known for exhibiting significantly higher volatility than traditional asset classes. Efficient and adequate risk calculation is vital for managing risk exposures in such market environments where extreme price fluctuations occur in short timeframes. The objective of this thesis is to build a real-time computation workflow that provides VaR estimates for non-linear portfolios of cryptocurrency derivatives. Many researchers have examined the predictive capabilities of time-series models within the context of cryptocurrencies. In this work, we applied three commonly used models - EMWA, GARCH and HAR - to capture and forecast volatility dynamics, in conjunction with delta-gamma-theta approach and Cornish-Fisher expansion to crypto derivatives, examining their performance from the perspectives of calculation efficiency and accuracy. We present a calculation workflow which harnesses the information embedded in high-frequency market data and the computation simplicity inherent in analytical estimation procedures. This workflow yields reasonably robust VaR estimates with calculation latencies on the order of milliseconds. ...

New general dependence measures: construction, estimation and application to high-frequency stock returns ArXiv ID: 2309.00025 “View on arXiv” Authors: Unknown Abstract We propose a set of dependence measures that are non-linear, local, invariant to a wide range of transformations on the marginals, can show tail and risk asymmetries, are always well-defined, are easy to estimate and can be used on any dataset. We propose a nonparametric estimator and prove its consistency and asymptotic normality. Thereby we significantly improve on existing (extreme) dependence measures used in asset pricing and statistics. To show practical utility, we use these measures on high-frequency stock return data around market distress events such as the 2010 Flash Crash and during the GFC. Contrary to ubiquitously used correlations we find that our measures clearly show tail asymmetry, non-linearity, lack of diversification and endogenous buildup of risks present during these distress events. Additionally, our measures anticipate large (joint) losses during the Flash Crash while also anticipating the bounce back and flagging the subsequent market fragility. Our findings have implications for risk management, portfolio construction and hedging at any frequency. ...

Optimal Execution Using Reinforcement Learning ArXiv ID: 2306.17178 “View on arXiv” Authors: Unknown Abstract This work is about optimal order execution, where a large order is split into several small orders to maximize the implementation shortfall. Based on the diversity of cryptocurrency exchanges, we attempt to extract cross-exchange signals by aligning data from multiple exchanges for the first time. Unlike most previous studies that focused on using single-exchange information, we discuss the impact of cross-exchange signals on the agent’s decision-making in the optimal execution problem. Experimental results show that cross-exchange signals can provide additional information for the optimal execution of cryptocurrency to facilitate the optimal execution process. ...

Permutation invariant Gaussian matrix models for financial correlation matrices ArXiv ID: 2306.04569 “View on arXiv” Authors: Unknown Abstract We construct an ensemble of correlation matrices from high-frequency foreign exchange market data, with one matrix for every day for 446 days. The matrices are symmetric and have vanishing diagonal elements after subtracting the identity matrix. For this case, we construct the general permutation invariant Gaussian matrix model, which has 4 parameters characterised using the representation theory of symmetric groups. The permutation invariant polynomial functions of the symmetric, diagonally vanishing matrices have a basis labelled by undirected loop-less graphs. Using the expectation values of the general linear and quadratic permutation invariant functions of the matrices in the dataset, the 4 parameters of the matrix model are determined. The model then predicts the expectation values of the cubic and quartic polynomials. These predictions are compared to the data to give strong evidence for a good overall fit of the permutation invariant Gaussian matrix model. The linear, quadratic, cubic and quartic polynomial functions are then used to define low-dimensional feature vectors for the days associated to the matrices. These vectors, with choices informed by the refined structure of small non-Gaussianities, are found to be effective as a tool for anomaly detection in market states: statistically significant correlations are established between atypical days as defined using these feature vectors, and days with significant economic events as recognized in standard foreign exchange economic calendars. They are also shown to be useful as a tool for ranking pairs of days in terms of their similarity, yielding a strongly statistically significant correlation with a ranking based on a higher dimensional proxy for visual similarity. ...

Volatility of Volatility and Leverage Effect from Options ArXiv ID: 2305.04137 “View on arXiv” Authors: Unknown Abstract We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options’ expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order autocovariance of the spot volatility increments, with the latter correcting for the bias in the former due to option observation errors. The leverage effect estimator is the sample covariance between price increments and the estimated volatility increments. The rate of convergence of the estimators depends on the diffusive innovations in the latent volatility process as well as on the observation error in the options with strikes in the vicinity of the current spot price. Feasible inference is developed in a way that does not require prior knowledge of the source of estimation error that is asymptotically dominating. ...