ABSTRACT
As is well known, multi-factor stochastic volatility models are necessary to capture the market accurately in pricing financial derivatives. However, the multi-factor models usually require too many parameters to be calibrated efficiently and they do not lead to an analytic pricing formula. The double Heston model is one of them. The approach of this paper for this difficulty is to rescale the double Heston model to reduce the number of the model parameters and obtain a closed form analytic solution formula for variance swaps explicitly. We show that the rescaled double Heston model is as effective as the original double Heston model in terms of fitting to the VIX market data in a stable condition and yet the computing time is much less than that under the double Heston model. However, in a turbulent situation after the start of the COVID-19 pandemic in 2020, we acknowledge that even the double Heston model fails to capture the market accurately.
ABSTRACT
BACKGROUND: Untact cultures have rapidly spread around the world as a result of the prolongation of the COVID-19 pandemic, leading to various types of research and technological developments in the fields of medicine and health care, where digital health care refers to health care services provided in a digital environment. Previous studies relating to digital health care demonstrated its effectiveness in managing chronic diseases such as hypertension and diabetes. While many studies have applied digital health care to various diseases, daily health care is needed for healthy individuals before they are diagnosed with a disease. Accordingly, research on individuals who have not been diagnosed with a disease is also necessary. OBJECTIVE: This study aimed to identify the effects of using a customized digital health care service (CDHCS) on risk factors for metabolic syndrome (MS) and lifestyle improvement. METHODS: The population consisted of 63 adults who underwent a health checkup at the National Health Insurance Service Ilsan (NHIS) Hospital in 2020. Measured variables include basic clinical indicators, MS-related variables, and lifestyle variables. All items were measured at NHIS Ilsan Hospital before the use of the CDHCS and 3 months thereafter. The CDHCS used in this study is a mobile app that analyzes the health condition of the user by identifying their risk factors and provides appropriate health care content. For comparison between before and after CDHCS use (pre-post comparison), paired t test was used for continuous variables, and a chi-square test was used for nominal variables. RESULTS: The study population included 30 (47.6%) male and 33 (52.4%) female participants, and the mean age was 47.61 (SD 13.93) years. The changes in clinical indicators before and after intervention results showed a decrease in weight, waist circumference, triglyceride, and high-density lipoprotein cholesterol and increases in systolic blood pressure and diastolic blood pressure. The distribution of the risk group increased from 32 (50.8%) to 34 (54%) and that of the MS group decreased from 18 (28.6%) to 16 (25.4%). The mean metabolic syndrome age-chronological age before the CDHCS was 2.20 years, which decreased to 1.72 years after CDHCS, showing a decrease of 0.48 years in the mean metabolic syndrome age-chronological age after the intervention. While all lifestyle variables, except alcohol consumption, showed a tendency toward improvement, the differences were not statistically significant. CONCLUSIONS: Although there was no statistical significance in the variables under study, this pilot study will provide a foundation for more accurate verification of CDHCS in future research.
ABSTRACT
The stochastic elasticity of variance model introduced by Kim et al. (Appl Stoch Models Bus Ind 30(6):753-765, 2014) is a useful model for forecasting extraordinary volatility behavior which would take place in a financial crisis and high volatility of a market could be linked to default risk of option contracts. So, it is natural to study the pricing of options with default risk under the stochastic elasticity of variance. Based on a framework with two separate scales that could minimize the number of necessary parameters for calibration but reflect the essential characteristics of the underlying asset and the firm value of the option writer, we obtain a closed form approximation formula for the option price via double Mellin transform with singular perturbation. Our formula is explicitly expressed as the Black-Scholes formula plus correction terms. The correction terms are given by the simple derivatives of the Black-Scholes solution so that the model calibration can be done very fast and effectively.
ABSTRACT
It is important to impose a persistent stochastic factor on the underlying asset model to obtain the fair value of financial derivatives with long time-to-maturities. Our empirical study, including the Covid-19 pandemic crisis period, indicates the presence of both fast and slow-scale in the elasticity of variance of S&P 500. This paper extends the elasticity in terms of multiscale stochastic process and obtains a closed form analytic pricing formula for European options and then derive the fair value of Equity-Linked-Annuity (ELA). The Mellin transform method for solving the relevant partial differential equations provides a computationally-efficient pricing formula for the options and the ELA. The prices can be easily calculated simply by taking derivatives of the Black–Scholes option price. Our results reveal the sensitivity of the ELA term structure to the fast-scale or slow-scale related group parameters.