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on Market Microstructure |
| By: | Felix Lokin; Fenghui Yu |
| Abstract: | This paper focuses on computing the fill probabilities for limit orders positioned at various price levels within the limit order book, which play a crucial role in optimizing executions. We adopt a generic stochastic model to capture the dynamics of the order book as a series of queueing systems. This generic model is state-dependent and also incorporates stylized factors. We subsequently derive semi-analytical expressions to compute the relevant probabilities within the context of state-dependent stochastic order flows. These probabilities cover various scenarios, including the probability of a change in the mid-price, the fill probabilities of orders posted at the best quotes, and those posted at a price level deeper than the best quotes in the book, before the opposite best quote moves. These expressions can be further generalized to accommodate orders posted even deeper in the order book, although the associated probabilities are typically very small in such cases. Lastly, we conduct extensive numerical experiments using real order book data from the foreign exchange spot market. Our findings suggest that the model is tractable and possesses the capability to effectively capture the dynamics of the limit order book. Moreover, the derived formulas and numerical methods demonstrate reasonably good accuracy in estimating the fill probabilities. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.02572&r=mst |
| By: | Ruijun Bu; Degui Li; Oliver Linton; Hanchao Wang |
| Abstract: | In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the highfrequency data contaminated by the microstructure noise, we introduce a localised pre-averaging estimation method in the high-dimensional setting which first pre-whitens data via a kernel filter and then uses the estimation tool developed in the noise-free scenario, and further derive the uniform convergence rates for the developed spot volatility matrix estimator. In addition, we also combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector, and establish the relevant uniform consistency result. Numerical studies are provided to examine performance of the proposed estimation methods in finite samples. |
| Keywords: | Brownian semi-martingale, Kernel smoothing, Microstructure noise, Sparsity, Spot volatility matrix, Uniform consistency. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:liv:livedp:202212&r=mst |
| By: | Konark Jain; Nick Firoozye; Jonathan Kochems; Philip Treleaven |
| Abstract: | Limit Order Books (LOBs) serve as a mechanism for buyers and sellers to interact with each other in the financial markets. Modelling and simulating LOBs is quite often necessary} for calibrating and fine-tuning the automated trading strategies developed in algorithmic trading research. The recent AI revolution and availability of faster and cheaper compute power has enabled the modelling and simulations to grow richer and even use modern AI techniques. In this review we \highlight{examine} the various kinds of LOB simulation models present in the current state of the art. We provide a classification of the models on the basis of their methodology and provide an aggregate view of the popular stylized facts used in the literature to test the models. We additionally provide a focused study of price impact's presence in the models since it is one of the more crucial phenomena to model in algorithmic trading. Finally, we conduct a comparative analysis of various qualities of fits of these models and how they perform when tested against empirical data. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.17359&r=mst |
| By: | Adele Ravagnani; Fabrizio Lillo; Paola Deriu; Piero Mazzarisi; Francesca Medda; Antonio Russo |
| Abstract: | Identification of market abuse is an extremely complicated activity that requires the analysis of large and complex datasets. We propose an unsupervised machine learning method for contextual anomaly detection, which allows to support market surveillance aimed at identifying potential insider trading activities. This method lies in the reconstruction-based paradigm and employs principal component analysis and autoencoders as dimensionality reduction techniques. The only input of this method is the trading position of each investor active on the asset for which we have a price sensitive event (PSE). After determining reconstruction errors related to the trading profiles, several conditions are imposed in order to identify investors whose behavior could be suspicious of insider trading related to the PSE. As a case study, we apply our method to investor resolved data of Italian stocks around takeover bids. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.00707&r=mst |
| By: | Sung Hoon Choi; Donggyu Kim |
| Abstract: | In this paper, we introduce a novel method for predicting intraday instantaneous volatility based on Ito semimartingale models using high-frequency financial data. Several studies have highlighted stylized volatility time series features, such as interday auto-regressive dynamics and the intraday U-shaped pattern. To accommodate these volatility features, we propose an interday-by-intraday instantaneous volatility matrix process that can be decomposed into low-rank conditional expected instantaneous volatility and noise matrices. To predict the low-rank conditional expected instantaneous volatility matrix, we propose the Two-sIde Projected-PCA (TIP-PCA) procedure. We establish asymptotic properties of the proposed estimators and conduct a simulation study to assess the finite sample performance of the proposed prediction method. Finally, we apply the TIP-PCA method to an out-of-sample instantaneous volatility vector prediction study using high-frequency data from the S&P 500 index and 11 sector index funds. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.02591&r=mst |
| By: | Peng Yifeng |
| Abstract: | In recent years, there has been quick developments of derivative markets in China and standardized derivative trading have reached considerable volumes. In this research, we collect all the daily data of ETF options traded at Shanghai Stock Exchange and start with a simple short-volatility strategy. The strategy delivers nice performance before 2018, providing significant excess return over the buy and hold benchmark. However, after 2018, this strategy starts to deteriorate and no obvious risk-adjusted return is shown. Based on the discussion of relationship between the strategy's performance and market's volatility, we improve the model by adjusting positions and exposure according to volatility forecasts using methods such as volatility momentum and GARCH. The new models have improved performance in different ways, where larger upside capture and smaller drawbacks can be achieved in market fluctuation. This research has shown potentials of volatility-based trading on Chinese equity index options, and with further improvement and implementation considerations, real-world practical trading strategies can be formed. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.00474&r=mst |