Advanced Modelling in Finance Using Excel and VBA

Chapter 14. Introduction to Valuing Options on Bonds

Valuing options on bonds is more complex than valuing derivatives on equities, since we are dealing with the term structure of interest rates. The term structure represents how the pattern of interest rates varies with bond maturity. The term structure is estimated from the prices of all bonds with different maturities that make up the bond market. The process of estimation is complicated in that most traded bonds consist of a stream of coupon payments (typically twice a year) followed by repayment of the face value of the bond at maturity. However some bonds repay the face value only with no intermediate coupons and these are known as zero-coupon bonds.

There are three distinct ways to allow for the term structure when valuing options on bonds: (i) ignore the term structure; (ii) model the term structure; and (iii) match the term structure. Valuing options on bonds has developed from attempts to adapt the Black–Scholes formula (the first way) through continuous models of interest rates (the second way) and is now centred on discrete models of interest rates that match the term structure (the third way).

In this chapter, we start by discussing the term structure of interest rates and the requirement to value coupon bond cash flows using appropriate discount factors. We describe how a simple binomial tree of interest rates can be devised to match the price of a zero-coupon bond in the market. Finally, Black's formula for the valuation ...