The purpose of this study include to perform data analysis by fitting with the measurement of the interest rate derivatives products, European style and Bermudan style swaptions. And the other purpose is to understand the model mathematically. Moreover, during the calibration process, we should construct a sense of understanding the major classes to the model(i.e. short rate, replicating portfolio, state price and swaption value). Therefore we demonstrate on the basis of which the driving factor is the short rate and that the logarithm of the short rate is normally distributed.
It can be seen that result in our study:
First, among the three tree-values, the discrepancy of the value of ∆t =1/4 is the smallest, Second, among the three tree-values, the discrepancy of the value of ∆t =1/2 is the greatest, Third, both the values of ∆t =1 and ∆t =1/2 are smaller than the Black-value.
It says that early exercise opportunity can be checked easily by means of tree model. It also shows that replicating strategy can be easily understood by tree model. Finally, the tree-values of the European payers swaption are compared with the Black-value. The result shows that the smallest ∆t gives value with the smallest discrepancy. However, the greatest ∆t does not give value with the greatest discrepancy.
