Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns risk appetite. To assess the statistical behavior of the time series, we run a series of preliminary analyses whose results suggest there is some long-range dependence in the VIX index. This is consistent with the strong empirical evidence in the literature supporting long memory in both options-implied and realized volatilities. We thus resort to linear and nonlinear heterogeneous autoregressive (HAR) processes, including smooth transition and threshold HAR-type models, as well as to smooth transition autoregressive trees (START) for modeling and forecasting purposes. The in-sample results for the HAR-type indicate that they cope with the long-range dependence in the VIX time series as well as the more popular ARFIMA model. In addition, the highly nonlinear START specification also does a god job in controlling for the long memory. The out-of-sample analysis evince that the linear ARMA and ARFIMA models perform very well in the short run and very poorly in the long-run, whereas the START model entails by far the best results for the longer horizon despite of failing at shorter horizons. In contrast, the HAR-type models entail reasonable relative performances in most horizons. Finally, we also show how a simple forecast combination brings about great improvements in terms of predictive ability for most horizons.heterogeneous autoregression, implied volatility, smooth transition, VIX.

Testing the Markov property with ultra-high frequency financial data

This paper develops a framework to nonparametrically test whether discretevalued irregularly-spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.Bid-ask spread, nonparametric testing, price durations, Markov property, ultra-high frequency data

Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity

This paper is devoted to global well-posedness, self-similarity and symmetries of solutions for a superdiffusive heat equation with superlinear and gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type spaces. Unlike the heat equation, we need to develop an appropriate decomposition of the two-parametric Mittag-Leffler function in order to obtain Mikhlin-type estimates get our well-posedness theorem. To the best of our knowledge, the present work is the first one concerned with a well-posedness theory for a time-fractional partial differential equations of order $\alpha\in(1,2)$ with non null initial velocity

Deglaciation chronology and post-glacial environmental evolution of the Upper Garonne valley (Central Pyrenees)

This PhD dissertation focuses on the Upper Garonne basin, Central Pyrenees. The study area ranges from the highest peaks at >2800-3000 m to the lowest moraine deposits located in the Loures Barousse Barbazan basin (LBBB) at 400-500 m. This catchment hosted the largest Quaternary glacier in the Pyrenees, although little was known about its glacial chronology. An accurate geomorphological analysis and mapping of the distribution of glacial and periglacial phenomena in the study area revealed the existence of a wide variety of landforms indicative of the occurrence of several periods of intense glacial and periglacial activity. The moraine distribution indicates that glaciers formed three moraine complexes at (1) moraines at the glacial terminal basin (420-820 m), (2) moraines at the mountain slopes and high valleys (1000-2100 m) and moraines at the glacial cirques (>2100 m). In the foreland of the Pyrenees, we find the LBBB, which includes the lowest moraine system of the Upper Garonne basin at 80 km from the headwaters of the catchment. Here, the external moraine (ca. 420 m) was dated by means of cosmic-ray exposure (CRE) and yielded an age of 128.5 ± 9.1 ka. This age constitutes the most solid chronological record of glacier advance in the Pyrenees during the Last Glacial Cycle and suggests that the past Equilibrium Line Altitude (palaeoELA) at that time was set at 1705 m and summer temperatures were ca. 9.3 ºC lower than the current values. The Garonne palaeoglacier must have also reached the LBBB during the Last Glacial Cycle (LGC), as confirmed by lake sediments from the Barbazan lake, although CRE results from boulders in the internal moraine system reported very scattered ages (73.1 ± 4.6 to 17.1 ± 1.8 ka). Such a large extension of the Garonne palaeoglacier during the global Last Glacial Maximum (GLGM) is also suggested by two CRE ages from the polished surfaces near the Marignac basin (7 km south of the LBBB). These ages of 24.2 ± 2.1 and 20.7 ± 1.2 ka indicate that this palaeoglacier was retreating during the GLGM while in Northern Europe, glaciers were still growing or at their maximum. The long-term recession was interrupted by brief periods of glacier expansion. No evidence has been dated yet of a glacial advance during the Oldest Dryas in this valley. Warm temperatures prevailing during the first half of the Bølling-Allerød (B-A) favoured a massive glacial retreat, with glaciers mostly disappearing from the highest catchments from 16.0 ± 1.0 to 13.5 ± 0.8 ka. During the late B-A and early Younger Dryas (YD), short episodes of lower temperatures and higher precipitation promoted glacial expansion and moraine formation, with 4.5 to 0.5-km-long glaciers advancing towards the high valley bottoms by 13.5 ± 0.9, 13.2 ± 1.1 and 13.0 ± 0.8 ka. These moraines are indicative of palaeoELAs up to 2461-2505 m and summer palaeotemperatures of 4.2-3.9 ºC lower than present-day. During the cold YD, small glaciers developed in the highest northern and western cirques by 12.8 ± 0.5 and 12.6 ± 1.3 ka. However, the increasing aridity during this stadial promoted their disappearance from larger cirques below 2800 m by 12.8 ± 0.8 and 12.7 ± 0.8 ka. During this short event, palaeoELAs were located at 2504-2571 m and summer palaeotemperatures of 3.4-3ºC lower than today. The deglaciation of the cirques and mountain slopes favoured paraglacial adjustment, triggering widespread slope failures and generating rock glaciers. In the Upper Garonne basin, paraglacial dynamics were largely controlled by lithology, as shown by the occurrence of large rock failures in the slates and lutites with limestones and rock glaciers in granitoids. The application of the CRE dating in rock glaciers showed that the glacial to periglacial transition was underway by 13.6 ± 0.9 ka, when rock glaciers started developing. These features stabilised soon after their formation and became relict by 11.9 ± 0.7 ka. During the cold phases of the Holocene, glaciers could have formed within sheltered areas in the highest cirques of the Central Pyrenees forming moraines above 2500 m, although no evidence has been found yet in the study area

The insurance industry in Brazil: a long-term view

This paper surveys the formation and development of insurance business in Brazil. It describes its very first steps, from the colonial times and imperial era to recent events. Particular attention is given to regulatory changes, showing how they evolved in response to macroeconomic shocks that affected the Brazilian economy during this period.Insurance, Brazil, Regulation. JEL Code: G22, G38, L50, N46.