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At least 307 records · Page 17Linked to original sources

arXiv2015

An optimal trading problem in intraday electricity markets

We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production.

q-fin.TR↗

arXiv2016

Foreign Exchange Market Microstructure and the WM/Reuters 4pm Fix

A market fix serves as a benchmark for foreign exchange (FX) execution, and is employed by many institutional investors to establish an exact reference at which execution takes place. The currently most popular FX fix is the World Market Reuters (WM/R) 4pm fix. Execution at the WM/R 4pm fix is a service offered by FX brokers (normally banks), who deliver execution at the fix provided they obtain the trade order until a certain time prior to 4pm. In this paper, we study the market microstructure around 4pm. We demonstrate that market dynamics can be distinguished from other times during the day through increased volatility and size of movements. Our findings question the aggregate benefit to the client base of using the 4pm fix in its current form.

q-fin.TR↗

arXiv2016

Quasi-Centralized Limit Order Books

A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. We perform an empirical analysis of a recent, high-quality data set from a large electronic trading platform that utilizes QCLOBs to facilitate trade. We find many significant differences between our results and those widely reported for other LOBs. We also uncover a remarkable empirical universality: although the distributions describing order flow and market state vary considerably across days, a simple, linear rescaling causes them to collapse onto a single curve. Motivated by this finding, we propose a semi-parametric model of order flow and market state in a QCLOB on a single trading day. Our model provides similar performance to that of parametric curve-fitting techniques, while being simpler to compute and faster to implement.

q-fin.TR↗

arXiv2015

Information and Trading Targets in a Dynamic Market Equilibrium

This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer who engages in order splitting to reach a cumulative trading target and an unconstrained strategic insider who trades on long-lived information. We consider cases in which the constrained rebalancer is partially informed as well as the special case in which the rebalancer is ex ante uninformed. We derive a linear Bayesian Nash equilibrium, describe an algorithm for computing such equilibria, and present numerical results on properties of these equilibria.

q-fin.TR↗

arXiv2015

Dark-Pool Perspective of Optimal Market Making

We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share commission no greater than the half bid-ask spread. Throughout the entire period, the main concern is inventory risk, which increases as the number of held positions becomes critically small or large. The dark pool can control its inventory by choosing the size of the commission for each transaction, so to encourage, e.g., buy orders instead of sell orders. Furthermore, it can submit lit-pool limit orders, of which execution is uncertain, and market orders, which are expensive. In either case, the dark pool risks an information leakage, which we model via a fixed penalty for trading in the lit pool. We solve a double-obstacle impulse-control problem associated with the optimal management of the inventory, and we show that the value function is the unique viscosity solution of the associated system of quasi variational inequalities. We explore various numerical examples of the proposed model, including one that admits a semi-explicit solution.

q-fin.MF↗

arXiv2016

A weak law of large numbers for a limit order book model with fully state dependent order dynamics

This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity. In the scaling limit the two volume densities follow each a non-linear PDE coupled with two non-linear ODEs that describe the best bid and ask price.

q-fin.MF↗

arXiv2015

A dynamic optimal execution strategy under stochastic price recovery

In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order, which is defined as a Cox process whose intensity increases by the degree of the market impact. We include not only the market order but also the limit order in our strategy in a restricted fashion. We formulate the problem as a combined stochastic control problem over a finite time horizon. The corresponding Hamilton-Jacobi-Bellman quasi-variational inequality is solved numerically. The optimal strategy obtained consists of three components: (i) the initial large trade; (ii) the unscheduled small trades during the period; (iii) the terminal large trade. The size and timing of the trade is governed by the tolerance for market impact depending on the state at each time step, and hence the strategy behaves dynamically. We also provide competitive results due to inclusion of the limit order, even though a limit order is allowed under conservative evaluation of the execution price.

q-fin.TR↗

arXiv2015

Hawkes processes in finance

In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular in empirical high frequency finance this last decade. After a reminder of the main definitions and properties that characterize Hawkes processes, we review their main empirical applications to address many different problems in high frequency finance. Because of their great flexibility and versatility, we show that they have been successfully involved in issues as diverse as estimating the volatility at the level of transaction data, estimating the market stability, accounting for systemic risk contagion, devising optimal execution strategies or capturing the dynamics of the full order book.

q-fin.TR↗

arXiv2015

Almost-sure hedging with permanent price impact

We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy.

q-fin.PR↗

arXiv2017

A Markov model of a limit order book: thresholds, recurrence, and trading strategies

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds. We make extensive use of fluid limits in order to establish recurrence properties of the model. We use the model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.

q-fin.TR↗

arXiv2015

Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes

We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+α)}$, with $α\in(0,1)$. We in particular prove that when $α\in(1/2,1)$, after suitable rescaling, their law converges to that of a kind of integrated fractional Cox-Ingersoll-Ross process, with associated Hurst parameter $H=α-1/2$. This result is in contrast to the case of a regression kernel with light tail, where a classical Brownian CIR process is obtained at the limit. Interestingly, it shows that persistence properties in the point process can lead to an irregular behavior of the limiting process. This theoretical result enables us to give an agent-based foundation to some recent findings about the rough nature of volatility in financial markets.

math.PR↗

arXiv2015

The Long Memory of Order Flow in the Foreign Exchange Spot Market

We study the long memory of order flow for each of three liquid currency pairs on a large electronic trading platform in the foreign exchange (FX) spot market. Due to the extremely high levels of market activity on the platform, and in contrast to existing empirical studies of other markets, our data enables us to perform statistically stable estimation without needing to aggregate data from different trading days. We find strong evidence of long memory, with a Hurst exponent of approximately 0.7, for each of the three currency pairs and on each trading day in our sample. We repeat our calculations using data that spans different trading days, and we find no significant differences in our results. We test and reject the hypothesis that the apparent long memory of order flow is an artifact caused by structural breaks, in favour of the alternative hypothesis of true long memory. We therefore conclude that the long memory of order flow in the FX spot market is a robust empirical property that persists across daily boundaries.

q-fin.TR↗

arXiv2015

Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs

This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analyze a related optimal switching problem that involves an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor generally enters when the price is low, but may find it optimal to wait if the current price is sufficiently close to zero. In other words, the continuation (waiting) region for entry is disconnected. Numerical results are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.

q-fin.TR↗

arXiv2015

Communication Strategies for Low-Latency Trading

The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two different regimes of channel noise for which: there is a unique Nash equilibrium yielding ties; and there are two Nash equilibria with different winners.

cs.IT↗

arXiv2015

Dynamics of Order Positions and Related Queues in a Limit Order Book

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a corollary, explicit analytical expressions for various quantities of interests in a limit order book are derived.

q-fin.TR↗

arXiv2015

Ergodicity and diffusivity of Markovian order book models: a general framework

We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic features of financial assets. To do so, we propose a new method of order book representation, and decompose the problem of order book modeling into two sub-problems: dynamics of a continuous-time double auction system with a fixed reference price; interactions between the double auction system and the reference price movements. State dependency is included in our framework by allowing the order flow intensities to depend on the order book state. Furthermore, contrary to most existing models, the impact of the order book updates on the reference price dynamics is not assumed to be instantaneous. We first prove that under general assumptions, our system is ergodic. Then we deduce the convergence towards a Brownian motion of the rescaled price process.

q-fin.TR↗

arXiv2015

Liquidity and Impact in Fair Markets

We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair price which corresponds to the average liquidation value (at the ask or the bid) of an infinitesimal quantity of stock. We show that this fair price is a natural reference price to compute the ex post gain of limit orders. Using only the fair market assumption, we link the spread to the impact of market orders on the fair price. We use our definition of the fair price to build empirical tests of the relevance of this notion whose results are consistent with our theoretical predictions.

q-fin.TR↗

arXiv2015

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.

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