**Unformatted text preview: **ANALYSIS OF BONDS WITH EMBEDDED
OPTIONS - CALLABLE BONDS REFERENCE:
Fabozzi, F.J. (2004). Bond Markets, Analysis and
Strategies, (5th ed) New Jersey: Prentice-Hall, Chapter 16, pp. 343-373. The notes that follow draw heavily from Fabozzi —
Chapter 16. DRAWBACKS OF TRADITIONAL YIELD
SPREAD ANALYSIS . Consider two 8.8 % coupon 25—year bonds paying
interest semi—annually; _ ' ($) MATURITY (%)
Treasury 915
Corporate 87.0798 10.24
The yield spread is difference between 10.24% and
9.15%, that is 1.09% or 109 basis points (BP). However, the traditional yield spread ignores the
0 term structure of interest rates 0 existence of embedded options ... callable/putable
bonds STATIC SPREAD: AN ALTERNATIVE TO YIELD
SPREAD DEMONSTRATION EXAMPLE: FABOZZI 16-2 Is the static spread for a three-year 9% coupon corporate
bond selling at $105.58 given the theoretical Treasury
spot rate below, 50, 100, or 200 basis points? SPOT RATE (%)
(NOTE RATE QUOTED PA.) 4.0 The static. spread is a measure of the spread an investor would realize over the entire Treasury spot rate curve if
the bond is HELD to MATURITY. The difference between the static spread and the
traditional yield curve increases with 0 increasing maturity 0 the steeper the yield curve
0 coupon rate 0 amortised (equal) cash ﬂows compared to bullet
payments CALLABLE BONDS AND THEIR INVESTMENT
CHARACTERISTICS The holder of callable bond has given the issuer the right
to call the issue prior to the expiration date. The presence of a call option has the following
disadvantages to the bondholder - Since an issuer will call a bond when the yield on the
bonds in the market is lower than the issue’s coupon
rate - the bondholder will be exposed to reinvestment
risk. it The price appreciation potential for a callable bond in
a declining interest rate environment is limited - price
compression. I PRICE-YIELD RELATIONSHIP EORVA
CALLABLE BOND ' Examine Exhibit 16— 4 As will be demonstrated later it is important to note that
a bond can trade above its call price even if 1t is likely to be called. COMPONENTS OF A BOND WITH AN
EMBEDDED OPTION Callable bond price w noncallable bond price
— call option price VALUATION MODEL The following approach Will be employed: - valuation of option-«free bonds; 0 introduction of interest rate volatility; 0 construction the binomial interest-rate tree; 0 application to valuation of an option—free bond;
0 valuation of a callable corporate bond; and o determination of the call option value VALUATION OF OPTION-«FREE BONDS Consider the following-hypothetical yield curve:
Yield to Maturity Market Value
(YearS) (%) ($) 1 3.50 100
2 4.00 100
3 4.50 100 By assuming annual coupon payments determine the
spot rate and one-year forward rate. INTEREST-RATE VOLATILITY Use the notation described in Fabozzi (2004:357—359). It is assumed that the one—year forward rate can evolve
based on a random process called a lognormal random
walk with a certain probability. Thus
__M 20‘
F} ,H "" 7” 1,L e
(7 == assumed volatility ofthe one—year forward-"rate
r131: = the lower onewyear rate one year from now;
7” 1H E the higher one-year rate one year from now In-the second year there are three possible values forghe
one-yearrate, F2,HH ,r2,HL and V2,” . It can be shown that: 40'
r2,LLe r2,HH and r2,HL r2,LLe We also will assume that there is an equal chance of
either an upward or downward movement in the interest
rates. CONSTRUCTING THE BINOMIAL INTEREST—
RATE TREE To obtain the bond’s value at a node we determine the
present value of the expected cash ﬂows by discounting
by the one-year forward rate at the node. Since at the node there is an equal: chance cf higher and
lower forward rate being present an average of the
present values is computed. " “f APPLICATION TO VALUING AN OPTION—FREE
BOND VALUING A CALLABLE CORPORATE BOND DETERNIINING THE CALL OPTION VALUE (OR
OPTION COST) Since Callable bond price w noncallable bond price
- call option price
then it follows Call option price = noncallable bond price
- call bond price ...

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- callable bond, callable bond price, noncallable bond price, callable corporate bond