Suppose an issuers binomial interest rate tree (10% volatility assumed) for valuing the issuers bond with four years to maturity, a coupon rate of 6.5%, and with a call price schedule is as shown below.

a. Find the theoretical value of the callable bond.

b. Suppose the market price of the callable bond is $103.125, what is the option-adjusted spread (OAS) of this bond relative to the issuers binomial interestrate tree (10% volatility assumed)?

c. What if the issuers interest rate tree is created with a 20% volatility assumption, would you expect the OAS to be smaller or larger than that computed in part b? Why?

Callable Bond Years To Maturity4 Coupon Rate | 6.50% Periods/Year1 Face Value [S1100 Coupon?! 6.5 Year 0 Year1 Year2 Year 3 Call Schedule NIA 102101 100 Binomial / Interest Rate Tree 3.5000% | 5.4289% | 7.0053% | 9.1987% 4.4448% | 5.7354% | 7.5312% | 4.6958% | 6.1660% 5.0483%