Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an eigenfunction expansion in eigenfunctions of the pricing operator with the expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump-diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a L\'{e}vy subordinator

Soluble neprilysin and long-term clinical outcomes in patients with coronary artery disease undergoing percutaneous coronary intervention: a retrospective cohort study

Background: Neprilysin has an essential role in regulating fluid balance and vascular resistance, and neprilysin inhibitors have shown beneficial effects in patients with heart failure. However, the potential predictive value of neprilysin levels as a biomarker for cardiovascular risk remains unclear. The aim of this study was to assess the prognostic value of soluble neprilysin (sNEP) levels in patients with ischemic heart disease. Methods: Neprilysin levels were measured in 694 consecutive patients with coronary artery disease (CAD) undergoing percutaneous coronary intervention (PCI). These patients were classified into two groups according to their serum levels of neprilysin and categorized into the lower neprilysin group (n = 348) and the higher neprilysin group (n = 346). The primary clinical endpoint was all-cause mortality, and the secondary endpoint was a composite of major adverse cardiac events (MACE). Results: The median sNEP level was 76.0 pg/ml. The median sNEP levels were higher in patients with left ventricular ejection fraction (LVEF) ≥40% (77.6 pg/ml, interquartile range 46.6–141.3) than in those with LVEF \u3c 40% (70.0 pg/ml, interquartile range 47.1–100.6; P = 0.032). Among all patients, each clinical outcome and MACE did not differ significantly according to the groups divided into median, tertile, or quartile of sNEP levels during a median follow-up of 28.4 months. We did not find a significant relationship between sNEP levels and clinical outcomes in multivariate Cox regression analysis. Among patients with LVEF \u3c 40%, an increased sNEP level was associated with a higher rate of all-cause death (adjusted hazard ratio 2.630, 95% confidence interval 1.049–6.595, P = 0.039). Conclusion: Serum sNEP levels are not associated with long-term mortality or cardiovascular outcomes after PCI in patients with CAD. In the LVEF \u3c 40% group, increased sNEP levels may be associated with a higher risk of all-cause death

Color Effects in Green Advertising

Marketers often use green in marketing communications to signal sustainability, despite the lack of supportive data. This article is a report of two experiments to observe consumer reactions to advertisements that use color to indicate environmental friendliness. The pretest and Study 1 confirm that consumers associate green with environmental friendliness and gray with environmental unfriendliness. Thus green (gray) is more (less) effective for producing positive ad attitudes and purchase intentions. Consumer perceptions regarding color appropriateness mediate the effects. Study 2 shows that persuasion knowledge moderates the effects: when consumers have high persuasive knowledge, green has a less positive effect; gray has a less negative effect; blue remains neutral. The study concludes that green functions as a peripheral cue signaling an eco‐friendly brand image, but the use of green may backfire when consumers are aware that green is used to bias responses