Analysis of Bonds with Embedded
Options
Zvi Wiener
Based on Chapter 14 in Fabozzi
Bond Markets, Analysis and Strategies
Fall-02
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
EMBAF
Static Spread
Yield difference is a bad measure of
profitability since it does not account for term
structure of IR and difference in cashflows.
Static spread: create an artificial cashflow
using zero-coupon IR, then calculate the
difference in yields.
See example in Exhibits 14-1, 14-2.
Zvi Wiener
Fabozzi Ch 14
slide 2
Callable Bond
price
Negative convexity area
non-callable
callable
yield
Callable bond = noncallable – call option price
Zvi Wiener
Fabozzi Ch 14
slide 3
Option-Free Bond
Price = present value of the cash flow
discounted at spot rates.
Years
1
2
3
YTM
3.5%
4.0%
4.5%
Market Value
100
100
100
Years
1
2
3
Spot rate
3.500%
4.010%
4.541%
Forward (1y)
3.500%
4.523%
5.580%
Zvi Wiener
Fabozzi Ch 14
slide 4
Option-Free Bond
5.25% coupon bond with 3 years to maturity:
$5.25 $5.25
$105.25


 102.075
2
3
1.035 1.0401 1.04541
$5.25
$5.25
$105.25


 102.075
1.035 1.035 1.04523 1.035 1.04523 1.05580
Zvi Wiener
Fabozzi Ch 14
slide 5
r3,HHH
r2,HH
r1,H
r3,HHL
r2,HL
r0
r1,L
r3,HLL
r2,LL
r3,LLL
Zvi Wiener
Fabozzi Ch 14
slide 6
r3e6
r2e4
r1e2
r3e4
r2e2
r0
r1
r3e2
r2
r3
Zvi Wiener
Fabozzi Ch 14
slide 7
r2, HH  r2, LL e 4
r2, HL  r2, LL e 2
Note that
Zvi Wiener
re 2  r r  2r  r

 r
2
2
Fabozzi Ch 14
slide 8
Zvi Wiener
Fabozzi Ch 14
slide 9
Option-Adjusted Spread OAS
OAS is the spread over the spot rate curve that
is due to the embedded options.
Modified duration often assumes fixed
cashflow.
A better measure is option-adjusted or
effective duration.
Zvi Wiener
Fabozzi Ch 14
slide 10
Effective Duration
P  P
Deffective 
2 P0 y
P- -price if yield is decreased by y
P+ -price if yield is increased by y
P0 – initial price of the bond
Zvi Wiener
Fabozzi Ch 14
slide 11
Effective Convexity
P  P  2 P0
Ceffective 
2
P0 y 
Zvi Wiener
Fabozzi Ch 14
slide 12
Home Assignment
Chapter 14
Ch. 14: Questions 2, 7, 13, 20, 22
Zvi Wiener
Fabozzi Ch 14
slide 13