145
CHAPTER 9
VALUATION AND
ANALYSIS: BONDS WITH
EMBEDDED OPTIONS
SOLUTIONS
style.
bonds to the issuer prior to maturity and to reinvest the proceeds of the retired bonds in
higher-yielding bonds.
is less likely to be put and thus behaves more like an option-free bond. C is also incorrect
because the e ective convexity of a putable bond is always positive. It is the e ective con-
vexity of a callable bond that will change from positive to negative if interest rates fall and
the call option is near the money.
146 Part II: Solutions
Year 0
Year 1
Year 3
Year 2
R = One-Year Interest Rate (%)
V = Value of the Putable Bond’s Future Cash Flows (% of par)
Year 0
Year 1
Year 3
Year 2
Chapter 9 Valuation and Analysis: Bonds with Embedded Options 147
ded put option, which is more likely to be exercised.
most likely result in more scenarios where the put option is exercised, which increases the
values calculated in the interest rate tree and, thus, the value of the putable bond.
lower forward rates, which increases the opportunities to call and, thus, the value of the
embedded call option.
However, the change in the convertible bond price is less than the change in the stock price
because the convertible bond has a oor—that oor is the value of the straight bond.
is not the case, the bond with the largest OAS (i.e., Bond #2) is likely to be underpriced
(cheap) relative to the bond with the smallest OAS (Bond #1).
equal to 1.
as interest rates rise, a put option moves into the money, which limits the price depreciation
of the putable bond and shortens its e ective duration. us, the bond whose e ective du-
ration will lengthen if interest rates rise is the callable bond, i.e., Bond #4.
using Exhibit 3 as follows:
148 Part II: Solutions
Year 0
Year 1
Year 3
Year 2
us, the e ective duration of Bond #4 is:
15 . A is correct:
Year 0
Year 1
Year 3
Year 2
Chapter 9 Valuation and Analysis: Bonds with Embedded Options 149
16 . C is correct:
Year 0
Year 1
Year 3
Year 2
value of Bond #10, the underlying option-free bond (straight bond), plus the value of a
call option on Whorton’s common stock.
bond (i.e., Bond #10).
e underlying share price ($30) is lower than the conversion price of Bond #9 ($50).
us, Bond #9 exhibits mostly bond risk-return characteristics and is least a ected by
Whorton’s common stock price movements.