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on Market Microstructure |
| By: | Stefan Gerhold; Paolo Guasoni; Johannes Muhle-Karbe; Walter Schachermayer |
| Abstract: | In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite-horizons. If the mean-variance ratio is constant, and price and volatility shocks uncorrelated, they are also robust to heteroskedasticity. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1108.1167&r=mst |
| By: | Bence Toth; Imon Palit; Fabrizio Lillo; J. Doyne Farmer |
| Abstract: | Equity order flow is persistent in the sense that buy orders tend to be followed by buy orders and sell orders tend to be followed by sell orders. For equity order flow this persistence is extremely long-ranged, with positive correlations spanning thousands of orders, over time intervals of up to several days. Such persistence in supply and demand is economically important because it influences the market impact as a function of both time and size and because it indicates that the market is in a sense out of equilibrium. Persistence can be caused by two types of behavior: (1) Order splitting, in which a single investor repeatedly places an order of the same sign, or (2) herding, in which different investors place orders of the same sign. We develop a method to decompose the autocorrelation function into splitting and herding components and apply this to order flow data from the London Stock Exchange containing exchange membership identifiers. Members typically act as brokers for other investors, so that it is not clear whether patterns we observe in brokerage data also reflect patterns in the behavior of single investors. To address this problem we develop models for the distortion caused by brokerage and demonstrate that persistence in order flow is overwhelmingly due to order splitting by single investors. At longer time scales we observe that different investors' behavior is anti-correlated. We show that this is due to differences in the response to price-changing vs. non-price-changing market orders. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1108.1632&r=mst |
| By: | Luciano Campi (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX, FiME - Laboratoire de Finance des Marchés d'Energies - Université Paris Dauphine - Paris IX); Umut Cetin (Department of Statistics, LSE - London School of Economics); Albina Danilova (Department of Mathematics, LSE - London School of Economics) |
| Abstract: | We consider an equilibrium model á la Kyle-Back for a defaultable claim issued by a given firm. In such a market the insider observes \emph{continuously in time} the value of firm, which is unobservable by the market maker. Using the construction of a dynamic Bessel bridge of dimension $3$ in Campi, \c Cetin and Danilova (2010), we provide the equilibrium price and the optimal insider's strategy. As in Campi and \c Cetin (2007), the information released by the insider while trading optimally makes the default time predictable in market's view at the equilibrium. We conclude the paper by comparing the insider's expected profits in the static and dynamic private information case. We also compute explicitly the value of insider's information in the special cases of a defaultable stock and a bond. |
| Date: | 2011–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00613216&r=mst |