The relationship between the volatility of returns and the number of jumps in financial markets

The contribution of this paper is two-fold. First we show how to estimate the volatility of high frequency log-returns where the estimates are not a affected by microstructure noise and the presence of Lévy-type jumps in prices. The second contribution focuses on the relationship between the number of jumps and the volatility of log-returns of the SPY, which is the fund that tracks the S&P 500. We employ SPY high frequency data (minute-by-minute) to obtain estimates of the volatility of the SPY log-returns to show that: (i) The number of jumps in the SPY is an important variable in explaining the daily volatility of the SPY log-returns; (ii) The number of jumps in the SPY prices has more explanatory power with respect to daily volatility than other variables based on: volume, number of trades, open and close, and other jump activity measures based on Bipower Variation; (iii) The number of jumps in the SPY prices has a similar explanatory power to that of the VIX, and slightly less explanatory power than measures based on high and low prices, when it comes to explaining volatility; (iv) Forecasts of the average number of jumps are important variables when producing monthly volatility forecasts and, furthermore, they contain information that is not impounded in the VIX.Volatility forecasts, High-frequency data, Implied volatility, VIX, Jumps, Microstructure noise

The relationship between the volatility of returns and the number of jumps in financial markets

The contribution of this paper is two-fold. First we show how to estimate the volatility of high frequency log-returns where the estimates are not affected by microstructure noise and the presence of Lévy-type jumps in prices. The second contribution focuses on the relationship between the number of jumps and the volatility of log-returns of the SPY, which is the fund that tracks the S&P 500. We employ SPY high frequency data (minute-by-minute) to obtain estimates of the volatility of the SPY log-returns to show that: (i) The number of jumps in the SPY is an important variable in explaining the daily volatility of the SPY log-returns; (ii) The number of jumps in the SPY prices has more explanatory power with respect to daily volatility than other variables based on: volume, number of trades, open and close, and other jump activity measures based on Bipower Variation; (iii) The number of jumps in the SPY prices has a similar explanatory power to that of the VIX, and slightly less explanatory power than measures based on high and low prices, when it comes to explaining volatility; (iv) Forecasts of the average number of jumps are important variables when producing monthly volatility forecasts and, furthermore, they contain information that is not impounded in the VIX

Subdiffusive Source Sensing by a Regional Detection Method.

Motivated by the fact that the danger may increase if the source of pollution problem remains unknown, in this paper, we study the source sensing problem for subdiffusion processes governed by time fractional diffusion systems based on a limited number of sensor measurements. For this, we first give some preliminary notions such as source, detection and regional spy sensors, etc. Secondly, we investigate the characterizations of regional strategic sensors and regional spy sensors. A regional detection approach on how to solve the source sensing problem of the considered system is then presented by using the Hilbert uniqueness method (HUM). This is to identify the unknown source only in a subregion of the whole domain, which is easier to be implemented and could save a lot of energy resources. Numerical examples are finally included to test our results

Revolutionaries and spies on trees and unicyclic graphs

A team of $r$ {\it revolutionaries} and a team of $s$ {\it spies} play a game on a graph $G$. Initially, revolutionaries and then spies take positions at vertices. In each subsequent round, each revolutionary may move to an adjacent vertex or not move, and then each spy has the same option. The revolutionaries want to hold an {\it unguarded meeting}, meaning $m$ revolutionaries at some vertex having no spy at the end of a round. To prevent this forever, trivially at least \min\{|V(G)|,\FL{r/m}\} spies are needed. When $G$ is a tree, this many spies suffices. When $G$ is a unicyclic graph, \min\{|V(G)|,\CL{r/m}\} spies suffice, and we characterize those unicyclic graphs where \FL{r/m}+1 spies are needed. \def\FL#1{\lfloor #1 \rfloor} \def\CL#1{\lceil #1 \rceil}Comment: 9 page

High resolution UVES/VLT spectra of white dwarfs observed for the ESO SN Ia Progenitor Survey III. DA white dwarfs

Original article can be found at: http://www.aanda.org/ Copyright The European Southern Observatory (ESO) DOI: 10.1051/0004-6361/200912531Context. The ESO Supernova Ia Progenitor Survey (SPY) took high-resolution spectra of more than 1000 white dwarfs and pre-white dwarfs. About two thirds of the stars observed are hydrogen-dominated DA white dwarfs. Here we present a catalog and detailed spectroscopic analysis of the DA stars in the SPY. Aims. Atmospheric parameters effective temperature and surface gravity are determined for normal DAs. Double-degenerate binaries, DAs with magnetic fields or dM companions, are classified and discussed. Methods. The spectra are compared with theoretical model atmospheres using a fitting technique. Results. Our final sample contains 615 DAs, which show only hydrogen features in their spectra, although some are double-degenerate binaries. 187 are new detections or classifications. We also find 10 magnetic DAs (4 new) and 46 DA+dM pairs (10 new).Peer reviewe