Using Riemann-Stieltjes methods for integrators of bounded p-variation we define a pathwise integral driven by a fractional Lévy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper integrals, the long-time behavior of FLPs is derived. This is sufficient to define the fractional Lévy-Ornstein-Uhlenbeck process (FLOUP) pathwise as an improper RiemannStieltjes integral. We show further that the FLOUP is the unique stationary solution of the corresponding Langevin equation. Furthermore, we calculate the autocovariance function and prove that its increments exhibit long-range dependence. Exploiting the Langevin equation, we consider SDEs driven by FLPs of bounded p-variation for p < 2 and construct solutions using the corresponding FLOUP. Finally, we consider examples of such SDEs, including various state space transforms of the FLOUP and also fractional Lévy-driven Cox-Ingersoll-Ross (CIR) models.

For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature that correlations and higher moments between different indices tend to vary in time. However, to the best of our knowledge, no one has yet considered a global setup including both equity and implied volatility indices of various continents, and allowing for a changing dependence structure. We aim to close this gap by applying Markov-switching R-vine models to investigate the existence of different, global dependence regimes. In particular, we identify times of "normal" and "abnormal" states within a data set consisting of North-American, European and Asian indices. Our results confirm the existence of joint points in a time at which global regime switching between two different R-vine structures takes place.

Background Strongylus vulgaris has become a rare parasite in Germany during the past 50 years due to the practice of frequent prophylactic anthelmintic therapy. To date, the emerging development of resistance in Cyathostominae and Parascaris spp. to numerous equine anthelmintics has changed deworming management and the frequency of anthelmintic usage. In this regard, reliable detection of parasitic infections, especially of the highly pathogenic S. vulgaris is essential. In the current study, two diagnostic methods for the detection of infections with S. vulgaris were compared and information on the occurrence of this parasite in German horses was gained. For this purpose, faecal samples of 501 horses were screened for S. vulgaris with real-time PCR and an additional larval culture was performed in samples of 278 horses. A subset of 26 horses underwent multiple follow-up examinations with both methods in order to evaluate both the persistence of S. vulgaris infections and the reproducibility of each diagnostic method.ResultsThe real-time PCR revealed S. vulgaris-DNA in ten of 501 investigated equine samples (1.9%). The larval culture demonstrated larvae of S. vulgaris in three of the 278 samples (1.1%). A direct comparison of the two methods was possible in 321 samples including 43 follow-up examinations with the result of 11 S. vulgaris-positive samples by real-time PCR and 4 S. vulgaris-positive samples by larval culture. The McNemar’s test (p-value = 0.016) revealed a significant difference and the kappa values (0.525) showed a moderate agreement between real-time PCR and larval culture.ConclusionsThe real-time PCR detected a significantly higher proportion of positives of S. vulgaris compared to larval culture and should thus be considered as a routine diagnostic method for the detection of S. vulgaris in equine samples.

Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.