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LOS 36.b: Explain the relationships between the READING 36: VALUATION AND ANALYSIS: BONDS WITH EMBEDDED OPTIONS
values of a callable or putable bond, the underlying
option-free (straight) bond, and the embedded option.
MODULE 36.1: TYPES OF EMBEDDED OPTIONS

The holder of a callable bond owns an option-free Conversely, investors are willing to pay a premium for a putable bond,
(straight) bond and is also short a call option written since its holder effectively owns an option-free bond plus a put option.
on the bond. The value of the embedded call option
(V call ) is, therefore, the difference between the value V = V + V
of a straight (V straight ) bond and the value of the putable straight put
comparable callable bond (V callable ): Rearranging: V put = V putable − V straight

V call = V straight − V callable

LOS 36.c: Describe how the arbitrage-free framework can be used to value a bond with embedded options.
LOS 36.f: Calculate the value of a callable or putable bond from an interest rate tree.

The process is similar to valuing a straight bond using BIRT but instead of using spot rates, one-period forward rates are used; this
computes the value of the bond at different points in time to determine if the embedded option is in-the-money!

Valuing a callable bond?
The value at any node where the bond is callable must be either the call price or the computed value if the bond if not called,
whichever is lower (the call rule: at node where par < ‘intrinsic’ price). Why lower?
Call is right to buy: you buy
lower, not higher!
Valuing a putable bond?
The value used at any node corresponding to a put date must be either the put price or the computed value if the bond is not put,
whichever is higher (the put rule: at node where par > ‘intrinsic’ price ). Why higher?
Put is the right to sell: you seller higher, not higher!