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on Market Microstructure |
| By: | Fabien Guilbaud (LPMA); Huy\^en Pham (LPMA, CREST) |
| Abstract: | We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.3051&r=mst |
| By: | Fei Chen (Huazhong University of Science and Technology); Francis X. Diebold (Department of Economics, University of Pennsylvania); Frank Schorfheide (Department of Economics, University of Pennsylvania) |
| Abstract: | We propose and illustrate a Markov-switching multi-fractal duration (MSMD) model for analysis of inter-trade durations in financial markets. We establish several of its key properties with emphasis on high persistence (indeed long memory). Empirical exploration suggests MSMD's superiority relative to leading competitors. |
| Keywords: | High-frequency trading data, point process, long memory, time deformation, scaling law, self-similarity, regime-switching model, market microstructure, liquidity |
| JEL: | C41 C22 G1 |
| Date: | 2012–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:12-020&r=mst |
| By: | Greg Farrell (South African Reserve Bank and Wits University); Shakill Hassan (South African Reserve Bank and University of Cape Town); Nicola Viegi (Department of Economics, University of Pretoria) |
| Abstract: | We examine the high-frequency response of the rand-dollar nominal rate within ten-minute intervals around five minutes before, five minutes after) official inflation announcements, and show that the rand appreciates (respectively, depreciates) on impact when inflation is higher (respectively, lower) than expected. The effect only applies after the adoption of inflation targeting, and is stronger for good news. Our findings are rationalisable by the belief, among market participants, in a credible (though perhaps not particularly aggressive) inflation targeting policy in South Africa; and can be used to monitor changes in currency market perceptions about the monetary policy regime. |
| Keywords: | High-frequency exchange rates, inflation surprises, Taylor rules, inflation targeting, credibility |
| JEL: | E31 E52 F30 F31 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201215&r=mst |
| By: | Mauricio Labadie; Charles-Albert Lehalle |
| Abstract: | We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Percentage of Volume, PVol) for both TC and IS. We also study an alternative set of risk measures for the optimisation of algorithmic trading curves. We assume a self-similar process (e.g. L\'evy process, fractional Brownian motion or fractal process) and define a new risk measure, the $p$-variation, which reduces to the variance if the process is a Brownian motion. We deduce the explicit formula for the TC and IS algorithms under a self-similar process. We show that there is an equivalence between self-similar models and a family of risk measures called $p$-variations: assuming a self-similar process and calibrating empirically the parameter $p$ for the $p$-variation yields the same result as assuming a Brownian motion and using the $p$-variation as risk measure instead of the variance. We also show that $p$ can be seen as a measure of the aggressiveness: $p$ increases if and only if the TC algorithm starts later and executes faster. From the explicit expression of the TC algorithm one can compute the sensitivities of the curve with respect to the parameters up to any order. As an example, we compute the first order sensitivity with respect to both a local and a global surge of volatility. Finally, we show how the parameter $p$ of the $p$-variation can be implied from the optimal starting time of TC, and that under this framework $p$ can be viewed as a measure of the joint impact of market impact (i.e. liquidity) and volatility. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.3482&r=mst |