Consider the following information about the current interest rate environment:

• 1-year spot rate: 4.0000%
• 2-year spot rate: 4.5113%
• 3-year spot rate: 5.0341%

Binomial Interest Rate Tree:

Year 0               Year 1               Year 2     

                                                  7.3734%

                         5.5286%

4.0000%                                    6.0368%

                         4.5264%

                                                  4.9425%

 

Additionally, a three-year callable bond with a 6% annual coupon is trading at 101.8386. If interest rate increases by 30 bps, the bond price will become 101.2545; if interest rate decreases by 30 bps, the price will be 102.2179.

 

Answer the following question:

1. What is the value of the option embedded in the callable bond?