Bonds with Options

Before we start, let's take a look at the basic principles behind bonds. A bond's yield is dependent on to major factors, the coupon rate (payments made semi-annually unless otherwise specified, analogous to interest payments) and the face value (analogous to repayment of principle). The combination of these two factors determines the yield to maturity (YTM) which is analogous to IRR in NPV and DCF (your calculator can actually use the same function to compute both as the math is identical). The relationships between these components are fairly intuitive and predictable (ceteris paribus):

• The higher the coupon, the higher the yield
• The higher the face value relative to the present value, the higher the yield
• The higher the yield, the lower the present value (and vise versa, Price and yield have an inverse relationship)
  

Note during this discussion that many of the mechanics relating to the treatment of options as they relate to equities also apply in the world of bonds as it relates to the value of the option. However, just to reiterate and clarify, let's look at each class of bond option seperately.

Callable Bonds
A callable option allows the borrower to pay the lender a specified amount to exit the bond agreement (benefits the borrower at a lower interest rate). This effectively acts as a ceiling price for the bond:

1. If the yield drops,
   
2. the cost of borrowing goes down, and
   
3. the price of the bond goes up.
4. If it passes the ceiling, the borrower will call the bond and issue a new bond at the lower rate.

This puts a cap on the maximum value of the bond.

Notice that the call option always benefits the lender, and this flexibility is paid for by issuing the bond at a lower price than an otherwise comparable straight bond at any given price. The nominal spread is always larger to account for the option. An option adjusted spread (OAS) is often approximated to understand the performance of the bond, excluding the option.

Putable Bonds
A putable bond option allows the lender to take a specified amount to exit the bond (benefits the lender at a higher interest rate). This acts as a price floor for the bond.

1. If the yield rises,
   
2. the cost of borrowing goes up, and
   
3. the price of the bond goes down.
4. If it passes the floor, the lender will put the bond and buy a new issue at the higher rate.

The price of a putable bond is always greater than a straight bond at any price point because of the inclusion of the put option (benefiting the lender).