Numerical studies of implied volatility expansions under the gatheral model

The Gatheral model is a three factor model with mean-reverting stochastic volatility that reverts to a stochastic long run mean. This chapter reviews previous analytical results on the first and second order implied volatility expansions under this model. Using the Monte Carlo simulation as the benchmark method, numerical studies are conducted to investigate the accuracy and properties of these analytical expansions. The classical Black-Scholes option pricing model assumes that the underlying asset follows a geometric Brownian motion with constant volatility. The chapter discusses partial calibration procedure is proposed and synthetic and real data calibration. If a full calibration is desired, we can use the results from the partial calibration as inputs for the final local optimization over all model parameters. In implementing the calibration procedure, the effect of the Covid-19 pandemic on the model calibration is high. © ISTE Ltd 2022.

p MEDICINES SOLD WITHOUT A PRESCRIPTION WITH A PLANT COMPONENT APPLIED AMONG CHILDREN DURING THE COVID-19 PANDEMIC

The interest in the practical use of herbal substances for medical purposes is growing worldwide. The herbal medicines can be applied as a supplement not only to restore the physiological functions but also to treat specific conditions such as -dyspepsia;hepatic and biliary diseases;prevent and modify cardiovascular diseases;treat infectious diseases. They are among the pharmaceutical products preferred by parents and pediatricians. In January 2020, the World Health Organization (WHO) declared the spread of the new coronavirus -a situation with a global impact. During the last year, there have been some publications describing the use of Chinese herbal preparations for the prevention and prophylaxis of COVID-19. There is information about the use of pharmaceuticals to treat infectious diseases and fever but real evidence for their impact on the SARS-CoV-2 virus is still insufficient. Therefore, the purpose of this study is to establish how many of the medicines sold without a prescription containing a plant component are used among very young children in Bulgaria and if these phytoproducts can be used to treat pediatric patients with COVID-19.