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on Market Microstructure |
| By: | Carla Ysusi |
| Abstract: | When the log-price process incorporates a jump component, realised variance will no longer estimate the integrated variance since its probability limit will be determined by the continuous and jump components. Instead realised bipower variation, tripower variation and quadpower variation are consistent estimators of integrated variance even in the presence of jumps. In this paper we derive the limit distributions of realised tripower and quadpower variation, allowing us to compare these three estimators of integrated variance. Using the limit theories for the differences of the errors, tests for jumps are proposed for each estimator. Using simulated data, the performance of each of these tests is compared. The tests are also applied to empirical data but results need to be taken carefully as market microstructure effects may contaminate real data. |
| Keywords: | Quadratic variation, Multipower variation, Stochastic volatility models, Jump process, Semimartingale, High-frequency data |
| JEL: | C12 C51 G19 |
| Date: | 2006–09 |
| URL: | http://d.repec.org/n?u=RePEc:bdm:wpaper:2006-10&r=mst |
| By: | Carla Ysusi |
| Abstract: | When high-frequency data is available, in the context of a stochastic volatility model, realised absolute variation can estimate integrated spot volatility. A central limit theory enables us to do filtering and smoothing using model-based and model-free approaches in order to improve the precision of these estimators. Although the absolute values are empirically attractive as they are less sensitive to possible large movements in high-frequency data, realised absolute variation does not estimate integrated variance. Some problems arise when using a finite number of intra-day observations, as explained here. |
| Keywords: | Quadratic variation, Absolute variation, Stochastic volatility models, Semimartingale, High-frequency data |
| JEL: | C13 C51 G19 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:bdm:wpaper:2006-13&r=mst |
| By: | Gaël Giraud (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | In this paper, a continuous-time price-quantity trading process is defined for exchange economies with differentiable characteristics. The dynamics is based on boundedly rational agents exchanging limit-price orders to a central clearing house, which rations infinitesimal trades according to Mertens (2003) double auction. Existence of continuous trade and price curves holds under weak conditions and in particular even if there is no long-run competitive equilibrium. Every such curve converges towards a Pareto point, and every Paretian allocation is a locally stable rest-point. Generically, given initial conditions, the trade and price curve is piecewise unique, smooth and computable, hence enables to effectively perform comparative dynamics. Finally, in the 2 x 2 case, the vector field induced by the limit-price dynamics is real-analytic. |
| Keywords: | Non-tatonnement, price-quantity dynamics, limit-price mechanism, myopia, computable general equilibrium. |
| Date: | 2007–06–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00155709_v1&r=mst |
| By: | Gaël Giraud (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | Static competitive equilibria in economies with incomplete markets are generically constrained suboptimal. Allocations induced by strategic equilibria of imperfectly competitive markets are also generically inefficient. In both cases, there is scope for Pareto-improving amendments. In an extension of the limit-price process introduced in Giraud [20] to incomplete markets (with infinitely many uncertain states) populated by finitely many players, we show that these two inefficiency problems can be partially overcome when rephrased in a non-tatonnement process. Traders are myopic and trade financial securities in continuous time by sending limit-orders so as to select a portfolio that maximizes the first-order approximation of their expected indirect utility. We show that financial trade curves exist and converge to some second-best efficient restpoint unless some miscoordination stops the dynamics at some inefficient, but locally unstable point. |
| Keywords: | Incomplet markets, imperfect competition, second-best efficiency, non-tatonnement. |
| Date: | 2007–06–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00155717_v1&r=mst |