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This paper proposes a new collection of affine jump-diffusion models for the valuation of VIX derivatives. The models have two distinctive features. First, we allow for a positive correlation between changes in the VIX and in its stochastic volatility to accommodate asymmetric volatility. Second, upward and downward jumps in the VIX are separately modeled to accommodate the possibility that investors react differently to good and bad surprises. Using the VIX futures and options data from July 2006 through January 2013, we find conclusive evidence for the benefits of including both asymmetric volatility and upward jumps in models of VIX derivatives pricing. We do not, however, find evidence supporting downward jumps.

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Objective: To evaluate longitudinal changes of the hyoid bone position and pharyngeal airway space after bimaxillary surgery in mandibular prognathism patients. Materials and Methods: Cone-beam computed tomography scans were taken for 25 mandibular prognathism patients before surgery (T0), 2 months after surgery (T1), and 6 months after surgery (T2). The positional displacement of the hyoid bone was assessed using the coordinates at T0, T1, and T2. Additionally, the volume of each subject's pharyngeal airway was measured. Results: The mean amount of posterior maxilla impaction was 3.76 ± 1.33 mm as the palatal plane rotated 2.04° ± 2.28° in a clockwise direction as a result of bimaxillary surgery. The hyoid bone moved backward (P < .05, P < .001) and downward (P > .05, P < .05) at 2 months and 6 months after surgery, while the total volume of the pharyngeal airway significantly decreased at the same time points (P < .001, P < .001). There was significant relationship between the changes of the hyoid bone position and airway volume at 2 months after surgery (P < .05). The change of the palatal plane angle was positively correlated to the decrease in the total airway volume (P < .001). Conclusions: The null hypothesis was rejected. The hyoid bone moved inferoposteriorly, and the pharyngeal airway volume decreased for up to 6 months after bimaxillary surgery. The decrease in the pharyngeal airway volume was correlated to the changes in the palatal plane inclination and the positional change of the hyoid bone.

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