An

investment firm specializing in fixed income has the following portfolio of bonds, all with

similar credit rating and

maturity of 3 years. 0 < T

1

< T

2

< .....< T

n

and T

j

denote

s

time

as end

of year j

when a call

and/or a put

can be exercised by the issuer.

Interest rate volatility in the

next 3 years are estimated as

(1) = 10%,

(2) = 15%,

(3) = 15%.

Bond

Issuer

Company

Coupon

Call

Dates

OAS

(in bps)

Call price

Embedded

Option

A

PacBrew

T

1

, T

2

18.3

At Par

Callable

B

AsaBrew

T

1

, T

2

21.7

At Par

Callable

C

Innovat

5%

T

1

, T

2

20.0

At 104%

Callable

D

Innovat

5%

T

1

, T

2

20.0

At 101%

Putable

E

TechCraf

Straight

F

Techcraf

Convertible

Note: Grey box indicates that no information is given.

(a)

Bonds A and B are from related companies in the same sector of the same country.

If there is

arbitrage opportunities, what long or short positions would you take with regards to

Bonds A

and B?

(b)

Given

that Treasury notes for 1, 2 and 3 year maturities have par coupon rates of 1%, 1.

8

%,

2.2

%, calibrate the 3

-

period BDT binomial tree for

Bonds C and D.

(c)

What are the

arbitrage

-

free prices of Bonds C and D?

(d)

Effective duration is the (unsigned, usually quoted as absolute value) slope of the embedded

option bond price curve with respect to the yield

-

to

-

maturity.

What is the sign of the

effective

duration of

D

less the effective duration of C,

especially when in

terest rate rises?

(e)

Bond E has a current market price of 99.95.

Bond F has a conversion price of

32

. Techcraf's

stock is currently selling at

16

per share.

What would be an approximate value of Bond ??