Category Financial Econometrics and Empirical Market Microstructure

How Tick Size Affects the High Frequency Scaling of Stock Return Distributions

Gianbiagio Curato and Fabrizio Lillo

Abstract We study the high frequency scaling of the distributions of returns for stocks traded at NASDAQ market as a function of the tick-to-price ratio. The tick-to-price ratio is a measure of an effective tick size. We find dramatic differences between distributions for assets with large and small tick-to-price ratio. The presence of returns clustering is evident for large tick size assets. The statistical differences between large and small tick size assets appear to reduce at higher time scales of observation. A possible way to explain returns dynamics for large tick size assets is the coupling of returns with bid-ask spread dynamics...

Read More

Statistical Properties of MRW Process

In order to demonstrate distinctive feature of MRW process, one can compare its realization with realization of geometric Brownian motion (original random walk model of Bachelier), which sample increments and path are shown in Figs. 1 and 2. Sample realizations of increments and path of MRW are shown in Figs. 3 and 4.

Comparing Fig. 3 with Fig. 1, one can notice significant differences in the way, which each process goes. When dynamics of increments of random walk (Fig. 1) are very regular and one can not observe large deviations from the mean value, the dynamics of MRW (Fig. 3) is much more intermittent, one can easily spot volatility clustering and large excursions (extreme events).

o

image170

О І I I , , , I

‘ 0 2000 4000 6000 8000

n

Fig. 1 Increments of geometrical Brownian motion for a =...

Read More

On Some Approaches to Managing Market Risk Using VaR Limits: A Note

Alexey Lobanov

Abstract Market risk has been traditionally considered in a single-period setting, with fixed positions in a static portfolio and losses caused by price volatility over a specified time horizon. In the real world, however, trading losses are generally a product of both position changes and adverse market movements. Market risk limits have been widely used in the industry for controlling both ex-ante and ex-post losses from traders’ actions, but the interplay of risk limits with risk measurement has been scarcely studied in the literature. This note aims to provide insights into the broad concepts of using limits in market risk management, as well as some approaches to setting and managing market risk limits in a dynamic setting.

Keywords Market risk • Positions limits • Tr...

Read More

Time-Warped Longest Common Subsequence (T-WLCS)

The basic idea is to unite both DTW and LCSS approaches (Guo and Siegelmann 2004)

f 0, _if _i = 0 _or_j = 0

cij = max {a-i, j, ci, j_i, c,-_ij_i + 1 ,_if_i, j >0, Qt = Cj (5)

: max Ci_i, j, cij_i} , _if_i, j > 0, Qi ф Cj

Example 1.C = 41516171, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 4 Example 2. C = 44556677, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8 Example 3. C = 4455661111177, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8

4 Granger-Causality

A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X-values provide statistically significant information about future values of Y (Granger 1969).

Read More

The Daniels Model (2003)

The first example of this model was presented in Daniels et al. (2003). After that there were a few papers published with an analysis of this model (Farmer et al. 2005, 2006). The main assumption of this model was that orders are come onto the market randomly. There are market orders that are executed immediately and limit orders, which are placed at a fixed price level and executed only when there is a counter-party on the market which wants to trade at this price. All orders have an intensity of incoming, an intensity of canceling, a volume and a price (see Fig. 1). All these parameters can be measured using empirical data, and this is the main advantage of this model. We try to create a model as in the original papers.

For the estimation of parameter a we calculated the difference betwe...

Read More

Empirical Description of Markets Around Shocks

A broad range of research works tries to give an empirical description for price jumps and analyze their statistical properties and the behaviour of market quantities around such events.

The attempt to compare shocks on different time scales is relatively little explored. Fan and Wang (2007), for example, used wavelets to identify jumps on multiple time scales, but the method is not used to compare shocks on different scales, but to detect shocks using a multiscale tool. On the other hand the attempt to investigate shocks and pre – and aftershock market behaviour is not novel. Lillo and Mantegna studied the relaxation dynamics of the occurrence of large volatility after volatility shocks (Lillo and Mantegna 2004), Zawadowski et al (2004) examined the evolution of price, volatility and the ...

Read More