We propose a robust and stable lattice method which permits to obtain very accurate American option prices in presence of CIR stochastic interest rate without any numerical restriction on its parameters. Numerical results show the reliability and the accuracy of the proposed method.

We consider the problem of pricing step double barrier options with binomial lattice methods. We introduce an algorithm, based on interpolation techniques, that is robust and efficient, that treats the "near barrier" problem for double barrier options and permits the valuation of step double barrier options with American features. We provide a complete convergence analysis of the proposed lattice algorithm in the European case.

Background and purpose: The purpose of this study was to investigate the role of risk factors in predicting the variation in carotid atherosclerosis at ultrasonographic follow-up and, therefore, its role in the progression of large-vessel disease. Methods: This retrospective population study included all the outpatients that underwent at least two carotid ultrasonographies at our laboratory from 2001 to 2017. Demographic data, vascular risk factors, and the results at follow-up were analysed to determine if correlations exist between these risk factors and variation in carotid atherosclerosis. Results: Data from 600 patients (327 males and 273 females with a mean age of 67 years) were collected. The mean follow-up period was 49 months (range: 1–195). We analysed each demographic variable and risk factor to assess its correlation with a worsening of carotid atherosclerosis; previous myocardial infarction (2.594), previous carotid surgical treatment (2.368), and hypertension (1.85) were found to have the highest odds ratios, respectively. Furthermore, the sample was divided into specific subpopulations (diabetes, hypertension, and smoking), and an association was found between age and worsening stenosis. Discussion and conclusions: Our results confirm the importance of carotid ultrasonographic follow-up in the monitoring and managing of large-vessel disease. Myocardial infarction, previous stroke, and previous surgical treatment were the strongest predictors of a worsening of carotid atherosclerosis. These findings suggest a strict follow-up is needed, even in the absence of significant carotid atherosclerosis at baseline.