|
on Market Microstructure |
| By: | Alexander Schied; Elias Strehle; Tao Zhang |
| Abstract: | We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic transaction costs of size $\theta\ge0$. We show that, for $\theta=0$, equilibrium strategies and costs will oscillate indefinitely between two accumulation points. For $\theta>0$, however, both strategies and costs will converge towards limits that are independent of $\theta$. We then show that the limiting strategies form a Nash equilibrium for a continuous-time version of the model with $\theta$ equal to a certain critical value $\theta^*>0$, and that the corresponding expected costs coincide with the high-frequency limits of the discrete-time equilibrium costs. For $\theta\neq\theta^*$, however, continuous-time Nash equilibria will typically not exist. Our results permit us to give mathematically rigorous proofs of numerical observations made in Schied and Zhang [arXiv:1305.4013, 2013]. In particular, we provide a range of model parameters for which the limiting expected costs of both agents are decreasing functions of $\theta$. That is, for sufficiently high trading speed, raising additional transaction costs can reduce the expected costs of all agents. |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1509.08281&r=all |
| By: | Enzo Busseti; Stephen Boyd |
| Abstract: | We study the problem of optimal execution of a trading order under Volume Weighted Average Price (VWAP) benchmark, from the point of view of a risk-averse broker. The problem consists in minimizing mean-variance of the slippage, with quadratic transaction costs. We devise multiple ways to solve it, in particular we study how to incorporate the information coming from the market during the schedule. Most related works in the literature eschew the issue of imperfect knowledge of the total market volume. We instead incorporate it in our model. We validate our method with extensive simulation of order execution on real NYSE market data. Our proposed solution, using a simple model for market volumes, reduces by 10% the VWAP deviation RMSE of the standard "static" solution (and can simultaneously reduce transaction costs). |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1509.08503&r=all |
| By: | Ilze KALNINA; Kokouvi TEWOU |
| Abstract: | This paper introduces a framework for analysis of cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Next, we study an idiosyncratic volatility factor model, in which we decompose the co-movements in idiosyncratic volatilities into two parts: those related to factors such as the market volatility, and the residual co-movements. When using high frequency data, naive estimators of all of the above measures are biased due to the estimation errors in idiosyncratic volatility. We provide bias-corrected estimators and establish their asymptotic properties. We apply our estimators to high-frequency data on 27 individual stocks from nine different sectors, and document strong cross-sectional dependence in their idiosyncratic volatilities. We also find that on average 74% of this dependence can be explained by the market volatility. |
| Keywords: | high frequency data, idiosyncratic volatility, factor structure, cross-sectional returns |
| JEL: | C22 C14 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:08-2015&r=all |
| By: | Yacine Aït-Sahalia; Dacheng Xiu |
| Abstract: | We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components and provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high frequency data at a time. The explanatory power of the high frequency principal components varies over time. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks. |
| JEL: | C22 C58 G01 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21584&r=all |
| By: | Adda, Jérôme |
| Abstract: | Viruses are a major threat to human health, and - given that they spread through social interactions - represent a costly externality. This paper addresses three main issues: i) what are the unintended consequences of economic activity on the spread of infections? ii) how efficient are measures that limit interpersonal contacts? iii) how do we allocate our scarce resources to limit their spread? To answer these questions, we use novel high frequency data from France on the incidence of a number of viral diseases across space, for different age groups, over a period of a quarter of a century. We use quasi-experimental variation to evaluate the importance of policies reducing inter-personal contacts such as school closures or the closure of public transportation networks. While these policies significantly reduce disease prevalence, we find that they are not cost-effective. We find that expansions of transportation networks have significant health costs in increasing the spread of viruses and that propagation rates are pro-cyclically sensitive to economic conditions and increase with inter-regional trade. |
| Keywords: | health; public policy; spatial diffusion; transportational networks |
| JEL: | C23 H51 I12 I15 I18 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10842&r=all |
| By: | Peter A. Bebbington; Reimer Kuehn |
| Abstract: | Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to a single traded asset and allows to find an optimal trading strategy which - for a given return - is minimally exposed to market price fluctuations. The model is initially investigated for a range of synthetic price processes, taken to be either second order stationary, or to exhibit second order stationary increments. Attention is paid to consequences of estimating auto-covariance matrices from small finite samples, and auto-covariance matrix cleaning strategies to mitigate against these are investigated. Finally we apply our framework to real world data. |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1509.07953&r=all |
| By: | Cathy Ning (Department of Economics, Ryerson University, Toronto, Canada); Dinghai Xu (Department of Economics, University of Waterloo, Waterloo, Ontario, Canada); Tony Wirjanto (School of Accounting & Finance and Department of Statistics & Actuarial Science,University of Waterloo, Waterloo, Ontario, Canada) |
| Abstract: | Volatility clustering is a well-known stylized feature of financial asset returns. In this paper, we investigate the asymmetric pattern of volatility clustering on both the stock and foreign exchange rate markets. To this end, we employ copula-based semi-parametric univariate time-series models that accommodate the clusters of both large and small volatilities in the analysis. Using daily realized volatilities of the individual company stocks, stock indices and foreign exchange rates constructed from high frequency data, we find that volatility clustering is strongly asymmetric in the sense that clusters of large volatilities tend to be much stronger than those of small volatilities. In addition, the asymmetric pattern of volatility clusters continues to be visible even when the clusters are allowed to be changing over time, and the volatility clusters themselves remain persistent even after forty days. |
| Keywords: | Volatility clustering, Copulas, Realized volatility, High-frequency data. |
| JEL: | C51 G32 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:rye:wpaper:wp050&r=all |