This section mainly introduces the implementation process of short-rate and discount, which is applied in Tree Swaption Engine. They are core part for option pricing. As part of Tree Engine, the class \(CIRModel\) implements the single-factor CIR model to calculate short-rate and discount by using continuous compounding. The implementation process is introduced as follows:
- Since the short-rate at the current time point is independent from the short-rate at the previous time point, there is no need to calculate the short-rate in this module.
- For implementing the generic Tree framework, this model only performs the calculation of some trinomial tree related parameters.
- The discount is calculated at time point \(t\) with the duration \(dt\) based on the short-rate.