We consider a single factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest and a forward rate to a fixed maturity. With this specification the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed form expression for bond prices. The prices of bond options are determined by a partial differential equation involving two spatial variables.

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Background: Our aim was to investigate whether early surgical preparation by reading an animated picture book about procedure-related events could reduce the preoperative anxiety in preschoolers.Methods: 131 patients, aged 3-6 years and underwent elective minor surgery were randomized either to a control or a picture book group. Both groups received general information about surgery and anesthesia in pre-anesthesia clinic. Patients in study group also received a surgery-depicting picture book for them to read at home a week earlier before surgery. Child anxiety was evaluated with the modified Yale Preoperative Anxiety Scale Short Form in six observing time points before anesthesia induction, and the compliance of anesthesia induction was assessed with the Induction Compliance Checklist (ICC).Results: There were significantly lower anxiety scores in picture book group than in control group at the time of ready for intravenous cannulation in operation room [51.9 (23.6) vs. 67.2 (22.0); P = 0.001] and at the time of pre-anesthesia visit [27.8 (7.6) vs. 33.2 (13.6); P = 0.018]. No significant differences of anxiety levels were found between two groups at other observed time points: in the anesthesia outpatient clinic, in the holding area, at separation from parent to operating room (OR), and on entrance to OR (P = 0.584, 0.335, 0.228, 0.137, respectively). The percentage of children with poor induction compliance (i.e., ICC ≥ 6) was higher in control group compared with that in picture book group (38% vs.21%, P = 0.041).Conclusions: Home-reading an animated picture book to get familiar with the perioperative events earlier prior to surgery could effectively reduce the preoperative anxiety level and increase the compliance during the induction of anesthesia in preschool children.Trial registration: ChiCTR2000033583, 06/06/2020 www.chictr.org.cn.