Options, Futures, and Other Derivatives, 7th Edition,
2
The day count convention
Interest earned between the two
dates
#days between dates
X Interest earned in
reference period
Treasury Bonds: Actual/Actual
(in period)
Corporate Bonds: 30/360
Money Market
Instruments:
Options, Futures, and Other Derivatives, 7th Edition,
4
Suppose that the bond principal is
$100, coupon payment dates are
March1 and September1, the coupon
rate is 8%, and we wish to calculate
the interest earned between March 1
and July 3. The reference period is
Cash price = Quoted price +
Cash price received by party with
short position =
Most recent settlement price ×
Conversion factor + Accrued interest
Options, Futures, and Other Derivatives 7th Edition,
The conversion factor for a bond is
approximately equal to the value of the
bond on the assumption that the yield
curve is flat at 6% with semiannual
Most recent settlement price = 90.00
Conversion factor of bond delivered =
1.3800
Accrued interest on bond =3.00
Price received for bond is
1.3800×90.00+3.00 = $127.20
per $100 of principal
Options, Futures, and Other Derivatives 7th Edition,
Short position receives
(Most recent settlement price X Conversion
factor) + Accrued interest
The cost of purchasing a bond
Quoted bond price + Accrued interest
The cheapest-to-deliver bond
A Eurodollar is a dollar deposited in a bank outside
the United States
Eurodollar futures are futures on the 3-month
Eurodollar deposit rate (same as 3-month LIBOR rate)
One contract is on the rate earned on $1 million
A change of one basis point or 0.01 in a Eurodollar
futures quote corresponds to a contract price change
of $25
A Eurodollar futures contract is settled in cash
When it expires (on the third Wednesday of the
delivery month) the final settlement price is 100
minus the actual three month deposit rate
Options, Futures, and Other Derivatives 7th Edition,
If
Q
is the quoted price of a Eurodollar
futures contract, the value of one
Eurodollar futures contracts last as long as
10 years
For Eurodollar futures lasting beyond two
years we cannot assume that the forward
rate equals the futures rate
Options, Futures, and Other Derivatives 7th Edition,
Futures is settled daily where forward is
settled once
Futures is settled at the beginning of the
A convexity adjustment often made is
Forward Rate=Futures Rate−0.5
2
T
1
T
2
T
1
is the time to maturity of the
forward contract
T
2
is the time to maturity of the rate
underlying the forward contract (90
days later that T
1
)
is the standard deviation of the short
rate (typically about 1.2%)
Options, Futures, and Other Derivatives, 7th Edition,
Maturity of
Futures
Convexity
Adjustment (bps)
2
3.2
4
12.2
6
27.0
8
47.5
LIBOR deposit rates define the LIBOR
zero curve out to one year
Eurodollar futures can be used to
determine forward rates and the forward
rates can then be used to bootstrap the
zero curve
Options, Futures, and Other Derivatives 7th Edition,
16
1
2
1
1
2
2
T
T
T
R
T
R
F
2
1
1
1
2
2
)
(
T
T
R
T
T
F
F
C
P
D
F
PD
F
C
Contract price for interest rate futures
D
F
Duration of asset underlying futures at
maturity
P
Value of portfolio being hedged
It is August. A fund manager has $10 million
invested in a portfolio of government bonds with a
duration of 6.80 years and wants to hedge against
interest rate moves between August and
December
The manager decides to use December T-bond
futures. The futures price is 93-02 or 93.0625 and
the duration of the cheapest to deliver bond is 9.2
years
The number of contracts that should be shorted is
Options, Futures, and Other Derivatives 7th Edition,
18
79
20
.
9
80
.
6
50
.
062
,
93
000
,
000
,
Assumes that only parallel shift in yield
curve take place
Assumes that yield curve changes are
small
When T-Bond futures is used assumes
