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```					          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
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
Negative convexity area
price

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      YTM           Market Value
1          3.5%          100
2          4.0%          100
3          4.5%          100
Years      Spot rate     Forward (1y)
1          3.500%        3.500%
2          4.010%        4.523%
3          4.541%        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
      2
       3
 102.075
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

r0                 r2,HL
r1,L                   r3,HLL
r2,LL

r3,LLL

Zvi Wiener          Fabozzi Ch 14            slide 6
r3e6

r2e4
r1e2                   r3e4

r0                  r2e2
r1                      r3e2
r2

r3

Zvi Wiener           Fabozzi Ch 14           slide 7
r2, HH  r2, LL e 4
r2, HL  r2, LL e 2

re 2  r r  2r  r
Note that                              r
2          2

Zvi Wiener                        Fabozzi Ch 14      slide 8
Zvi Wiener   Fabozzi Ch 14   slide 9
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 
P0 y 
2

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

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