Categorical Functional Data Analysis. The cfda R Package

Categorical functional data represented by paths of a stochastic jump process with continuous time and a finite set of states are considered. As an extension of the multiple correspondence analysis to an infinite set of variables, optimal encodings of states over time are approximated using an arbitrary finite basis of functions. This allows dimension reduction, optimal representation, and visualisation of data in lower dimensional spaces. The methodology is implemented in the cfda R package and is illustrated using a real data set in the clustering framework.

Time-Varying Skew in VIX Derivatives Pricing

This paper proposes a new reduced-form model for the pricing of VIX derivatives that includes an independent stochastic jump intensity factor and cojumps in the level and variance of VIX, while allowing the mean of VIX variance to be time varying. I fit the model to daily prices of futures and European options from April 2007 through December 2017. The empirical results indicate that the model significantly outperforms all other nested models and improves on benchmark by 21.6% in sample and 31.2% out of sample. The model more accurately portrays the tail behavior of VIX risk-neutral distribution for both short and long maturities, as it better captures the time-varying skew found to be largely independent of the level of the VIX smile. This paper was accepted by Kay Giesecke, finance.

Increased transmissibility of emerging SARS-CoV-2 variants is driven either by viral load or probability of infection rather than environmental stability

Understanding the factors that increase the transmissibility of the recently emerging variants of SARS-CoV-2 (such as the Alpha, Epsilon, and Delta variants) can aid in mitigating their spread. The enhanced transmissibility could be attributed to one or more factors: higher stability on surfaces or within droplet nuclei suspended in air, increased maximal viral load or higher probability of infection. The relative importance of these factors on the transmission was examined using a validated stochastic-jump-continuous hybrid model. The transmissibility was quantified in terms of the household secondary attack rate (hSAR) which is the probability of transmission from an infected individual to a susceptible one in a household. We find that an increase in either the maximal viral load or the probability of infection is consistent with the observed hSAR of the variants. Specifically, in order to reach the relative increase in the hSAR of 40%, 55%, and 87% reported for the Epsilon, Alpha, and Delta variants (respectively), the maximal viral load should increase by 56%, 78%, and 125%, respectively. Alternatively, the probability of infection should increase by 34%, 53%, and 193%, respectively. Contrary to these results, even a dramatic increase in environmental stability increases hSAR by no more than 10%.

Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

The dynamical system containing flag-shaped hysteretic behavior is common in practice. In this paper, the stationary response of flag-shaped hysteretic system excited by harmonic excitation as well as Gaussian white noise is determined with the technique of stochastic averaging. The reliability of the presented approach is demonstrated by relevant digital simulation. The stochastic jump under a certain combination of parameters is found. The stochastic P-bifurcation phenomenon, i.e., the disappearance or appearance of bimodal shape of stationary response, occurs concerning to the variation of system’s parameters. Besides, the response of the system exposed to only harmonic excitation or non-resonance case is also examined for comparison, respectively. The numerical results show that the stationary amplitude response displays typical “soft” system behavior, and the deterministic jump may occur under pure harmonic excitation. Moreover, the non-resonance response is always weaker than that of resonant case.