SEARCH · Searcharxiv

Results for “q-fin.TR”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19Linked to original sources

arXiv2015

Sequential Detection of Market shocks using Risk-averse Agent Based Models

This paper considers a statistical signal processing problem involving agent based models of financial markets which at a micro-level are driven by socially aware and risk- averse trading agents. These agents trade (buy or sell) stocks by exploiting information about the decisions of previous agents (social learning) via an order book in addition to a private (noisy) signal they receive on the value of the stock. We are interested in the following: (1) Modelling the dynamics of these risk averse agents, (2) Sequential detection of a market shock based on the behaviour of these agents. Structural results which characterize social learning under a risk measure, CVaR (Conditional Value-at-risk), are presented and formulation of the Bayesian change point detection problem is provided. The structural results exhibit two interesting prop- erties: (i) Risk averse agents herd more often than risk neutral agents (ii) The stopping set in the sequential detection problem is non-convex. The framework is validated on data from the Yahoo! Tech Buzz game dataset.

math.OC↗

arXiv2015

Modeling Market Inefficiencies within a Single Instrument

In this paper, we propose a minimal model beyond geometric Brownian motion that aims to describe price actions with market inefficiency. From simple financial theory considerations, we arrive at a simple two-variable hidden Markovian time series model, with one of the variable entirely unobserved. Then, we analyze the simplest version of the model, using path integral and Green's function techniques from physics. We show that in this model, the inefficient market price is trend-following when the standard deviation of the log reasonable price ($σ$) is larger than that of the log market price ($σ'$), and mean-reversing when it is smaller. The risk premium is proportional to the difference between the current market price and the exponential moving average (EMA) of the past prices. This model thus provides a theoretical explanation how the EMA of the past price can directly affect future prices, i.e., the so-called ``Bollinger bands" in technical analyses. We then carry out a maximum likelihood estimate for the model parameters from the observed market price, by integrating out the reasonable price in Fourier space. Finally we analyze recent S\&P500 index data and see to what extent the real world data can be described by this simple model.

q-fin.TR↗

arXiv2016

A Stochastic Model of Order Book Dynamics using Bouncing Geometric Brownian Motions

We consider a limit order book, where buyers and sellers register to trade a security at specific prices. The largest price buyers on the book are willing to offer is called the market bid price, and the smallest price sellers on the book are willing to accept is called the market ask price. Market ask price is always greater than market bid price, and these prices move upwards and downwards due to new arrivals, market trades, and cancellations. We model these two price processes as "bouncing geometric Brownian motions (GBMs)", which are defined as exponentials of two mutually reflected Brownian motions. We then modify these bouncing GBMs to construct a discrete time stochastic process of trading times and trading prices, which is parameterized by a positive parameter $δ$. Under this model, it is shown that the inter-trading times are inverse Gaussian distributed, and the logarithmic returns between consecutive trading times follow a normal inverse Gaussian distribution. Our main results show that the logarithmic trading price process is a renewal reward process, and under a suitable scaling, this process converges to a standard Brownian motion as $δ\to 0$. We also prove that the modified ask and bid processes approach the original bouncing GBMs as $δ\to0$. Finally, we derive a simple and effective prediction formula for trading prices, and illustrate the effectiveness of the prediction formula with an example using real stock price data.

q-fin.TR↗

arXiv2016

Latency and liquidity provision in a limit order book

We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book (LOB) before and after the arrival of a market order. For each of the stocks that we study, we identify a sequence of distinct phases across which the net flow of orders differs considerably. We note some of our results are consist with the widely reported phenomenon of stimulated refill, but that others are not. We therefore propose alternative mechanical and strategic motivations for the behaviour that we observe. Based on our findings, we argue that strategic liquidity providers consider both adverse selection and expected waiting costs when deciding how to act.

q-fin.TR↗

arXiv2016

Optimal Trading with Linear and (small) Non-Linear Costs

We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading speed vanishes inside a band that is narrower than in the absence of quadratic costs, by an amount that scales as the one-third power of quadratic costs. Outside of the band, we find three regimes: a small boundary layer where the velocity vanishes linearly with the distance to the band, an intermediate region where the velocity behaves as a square-root of that distance, and a far region where it becomes linear. Our solution is consistent with available numerical results. We determine the conditions in which our expansion is useful in practical applications, and generalize our solution to other forms of non-linear costs.

q-fin.TR↗

arXiv2017

The behavior of dealers and clients on the European corporate bond market: the case of Multi-Dealer-to-Client platforms

For the last two decades, most financial markets have undergone an evolution toward electronification. The market for corporate bonds is one of the last major financial markets to follow this unavoidable path. Traditionally quote-driven i.e., dealer-driven) rather than order-driven, the market for corporate bonds is still mainly dominated by voice trading, but a lot of electronic platforms have emerged. These electronic platforms make it possible for buy-side agents to simultaneously request several dealers for quotes, or even directly trade with other buy-siders. The research presented in this article is based on a large proprietary database of requests for quotes (RFQ) sent, through the multi-dealer-to-client (MD2C) platform operated by Bloomberg Fixed Income Trading, to one of the major liquidity providers in European corporate bonds. Our goal is (i) to model the RFQ process on these platforms and the resulting competition between dealers, and (ii) to use our model in order to implicit from the RFQ database the behavior of both dealers and clients on MD2C platforms.

q-fin.ST↗

arXiv2016

Optimal Real-Time Bidding Strategies

The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the \textit{price to beat} for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out.

math.OC↗

arXiv2015

Queue Imbalance as a One-Tick-Ahead Price Predictor in a Limit Order Book

We investigate whether the bid/ask queue imbalance in a limit order book (LOB) provides significant predictive power for the direction of the next mid-price movement. We consider this question both in the context of a simple binary classifier, which seeks to predict the direction of the next mid-price movement, and a probabilistic classifier, which seeks to predict the probability that the next mid-price movement will be upwards. To implement these classifiers, we fit logistic regressions between the queue imbalance and the direction of the subsequent mid-price movement for each of 10 liquid stocks on Nasdaq. In each case, we find a strongly statistically significant relationship between these variables. Compared to a simple null model, which assumes that the direction of mid-price changes is uncorrelated with the queue imbalance, we find that our logistic regression fits provide a considerable improvement in binary and probabilistic classification for large-tick stocks, and provide a moderate improvement in binary and probabilistic classification for small-tick stocks. We also perform local logistic regression fits on the same data, and find that this semi-parametric approach slightly outperform our logistic regression fits, at the expense of being more computationally intensive to implement.

q-fin.TR↗

arXiv2015

Using machine learning for medium frequency derivative portfolio trading

We use machine learning for designing a medium frequency trading strategy for a portfolio of 5 year and 10 year US Treasury note futures. We formulate this as a classification problem where we predict the weekly direction of movement of the portfolio using features extracted from a deep belief network trained on technical indicators of the portfolio constituents. The experimentation shows that the resulting pipeline is effective in making a profitable trade.

q-fin.TR↗

arXiv2015

On Optimal Pricing Model for Multiple Dealers in a Competitive Market

In this paper, the optimal pricing strategy in Avellande-Stoikov's for a monopolistic dealer is extended to a general situation where multiple dealers are present in a competitive market. The dealers' trading intensities, their optimal bid and ask prices and therefore their spreads are derived when the dealers are informed the severity of the competition. The effects of various parameters on the bid-ask quotes and profits of the dealers in a competitive market are also discussed. This study gives some insights on the average spread, profit of the dealers in a competitive trading environment.

q-fin.TR↗

arXiv2016

A Semi-Markovian Modeling of Limit Order Markets

R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their framework to 1) arbitrary distributions for book events inter-arrival times (possibly non-exponential) and 2) both the nature of a new book event and its corresponding inter-arrival time depend on the nature of the previous book event. We do so by resorting to Markov renewal processes to model the dynamics of the bid and ask queues. We keep analytical tractability via explicit expressions for the Laplace transforms of various quantities of interest. We justify and illustrate our approach by calibrating our model to the five stocks Amazon, Apple, Google, Intel and Microsoft on June 21^{st} 2012. As in R. Cont and A. de Larrard, the bid-ask spread remains constant equal to one tick, only the bid and ask queues are modeled (they are independent from each other and get reinitialized after a price change), and all orders have the same size.

q-fin.MF↗

arXiv2016

Deep Learning for Limit Order Books

This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new architecture yields a low-dimensional model of price movements deep into the limit order book, allowing more effective use of information from deep in the limit order book (i.e., many levels beyond the best bid and best ask). This "spatial neural network" models the joint distribution of the state of the limit order book at a future time conditional on the current state of the limit order book. The spatial neural network outperforms other models such as the naive empirical model, logistic regression (with nonlinear features), and a standard neural network architecture. Both neural networks strongly outperform the logistic regression model. Due to its more effective use of information deep in the limit order book, the spatial neural network especially outperforms the standard neural network in the tail of the distribution, which is important for risk management applications. The models are trained and tested on nearly 500 stocks. Techniques from deep learning such as dropout are employed to improve performance. Due to the significant computational challenges associated with the large amount of data, models are trained with a cluster of 50 GPUs.

q-fin.TR↗

arXiv2016

General Equilibrium and Recession Phenomenon

The theorems we proved describe the structure of economic equilibrium in the exchange economy model. We have studied the structure of property vectors under given structure of demand vectors at which given price vector is equilibrium one. On this ground, we describe the general structure of the equilibrium state and give characteristic of equilibrium state describing economic recession. The theory developed is applied to explain the state of the economy in some European countries.

econ.GN↗

arXiv2016

Testing for Causality in Continuous Time Bayesian Network Models of High-Frequency Data

Continuous time Bayesian networks are investigated with a special focus on their ability to express causality. A framework is presented for doing inference in these networks. The central contributions are a representation of the intensity matrices for the networks and the introduction of a causality measure. A new model for high-frequency financial data is presented. It is calibrated to market data and by the new causality measure it performs better than older models.

stat.ML↗

arXiv2016

Trading Strategy with Stochastic Volatility in a Limit Order Book Market

In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the controlled state process is the dealer's mark-to-market wealth. Dealers in the security market can optimally determine their ask and bid quotes on the underlying stocks or options continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost.

q-fin.TR↗

arXiv2016

Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact

Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description -- the History Dependent Impact Model (HDIM) -- assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.

q-fin.TR↗

arXiv2016

Unravelling the trading invariance hypothesis

We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades $N$. We show that this 3/2-law holds very precisely across 12 futures contracts and 300 single US stocks, and across a wide range of time scales. However, we find that the "trading invariant" $I=W/N^{3/2}$ proposed by Kyle and Obizhaeva is in fact quite different for different contracts, in particular between futures and single stocks. Our analysis suggests $I/{\cal C}$ as a more natural candidate, where $\cal C$ is the average spread cost of a trade, defined as the average of the trade size times the bid-ask spread. We also establish two more complex scaling laws for the volatility $σ$ and the traded volume $V$ as a function of $N$, that reveal the existence of a characteristic number of trades $N_0$ above which the expected behaviour $σ\sim \sqrt{N}$ and $V \sim N$ hold, but below which strong deviations appear, induced by the size of the~tick.

q-fin.TR↗

arXiv2016

The square-root impact law also holds for option markets

Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of option trades. We find that the square-root law indeed holds in that case. This finding supports the argument for a universal underlying mechanism.

q-fin.TR↗