Analysis of the bond issue
(a) Show that the price of the bond is equal to that of a portfolio which contains
i) a long position in an option-free but otherwise identical coupon bond, and
ii) a long position in a 5Y European put option written on that option-free coupon bond. What is the strike price of that put option? What is the value of the putable bond at the put date?
Assume that K = 1 and consider two option-free bonds both of which have annual coupon rate C paid in two semiannual installments and assume that the second bond has a maturity of 5 years while the second bond has a maturity of 10 years.
(b) Show that the price of RLC's bond is always higher than the maximum of the prices of these two bonds.
(c) Explain why the price of the putable bond approaches the price of the shorter straight bond as interest rates increase and the price of the longer straight bond as interest rates decrease. What impact does this have on the duration and the convexity of the bond? Brief explain.
The yield to put on a putable bond is the yield offered by the bond under the assumption that the put option will definitely be exercised. In contrast, the yield to maturity on a putable bond is the yield offered by the bond under the assumption that the put option will not be exercised.
(d) Explain why, contrary to what some practitioners believe, putable bonds can- not be priced on the basis of the yield to put when interest rates are high, and on the basis of the yield to maturity when interest rates are low.