forward and futures contracts
DESCRIPTION
FORWARD AND FUTURES CONTRACTS. Obligation to buy or sell an asset at a future date at a price that is stipulated now Since no money changes hands now, contract value should be zero - PowerPoint PPT PresentationTRANSCRIPT
FORWARD AND FUTURES CONTRACTS
Obligation to buy or sell an asset at a future date at a price that is stipulated now
Since no money changes hands now, contract value should be zero
Futures contracts distinguished from forwards by standardization and marking-to- market, but in our analysis we will treat the two contracts as if they were the same
NO-ARBITRAGE SPOT-FORWARD PRICING RELATIONSHIP
F0T = forward price on underlying asset to be delivered at T
S0 = spot price of underlying asset
Assume: underlying asset makes no cash payments between now and T
Tf0T0 )r1(SF
WHAT IF IT DOESN’T HOLD?
If F0T > S0(1+rf)T:
• Borrow S0
• Buy underlying asset• Sell underlying asset
for future delivery
If F0T < S0(1+rf)T:
• Sell underlying asset short
• Invest in riskless asset• Buy underlying asset
for future delivery
EXAMPLE: 1 and 2-PERIOD ZEROS
)r1(SF i.e., )y1()y1(
1
f1
1
)y1/(1 price zero period2 )f1/(1icePr Forward
)f1)(y1()y1(
f0011221
221
112
2
T-BILL SPOT FUTURES ARBITRAGE
Buy long bill Receive 1 mil139 days
48 days 91 days
8/5 9/22 12/22
Buy short bill Use short bill proceeds Receive 1 milBuy Sept. futures to settle futures purchase
T-BILL SPOT FUTURES ARBITRAGE
365
48
S
365
139
L365
91
fut
Tf0T0
)y1(x
)y1(
1
)y1(
1
)r1( x S F
T-BILL SPOT FUTURES ARBITRAGE
Long Bill (due 12/22)
discount = 4.48
Price =
(1-.0448(139/360))mil
= 982,702.22
Short Bill (due 9/22)
discount = 4.13
Price =
(1-.0413(48/360))
=.99449333
T-BILL SPOT FUTURES ARBITRAGE
Futures (due 9/22)
Quote = 95.38
discount = 100-95.38 = 4.62
Price =
(1-.0462(91/360))mil
= 988,321.67
Buy 1 mil face val. long bills: 982,702.22
Buy 988,321.67 face value short bills: .99449333(988321.67) = $982,879.31
Buy 1 mil face 91 day bills for delivery 9/22: 988,321.67
SPOT-FORWARD PRICING (Underlying asset has cash payout)
• Discrete-time version
= cash flow payout rate (e.g., dividend yield)
T
f0T0 1
r1SF
Application: COVERED INTEREST ARBITRAGE
bills £ :asset Underlying
)r1(
)r1(
£
$
£
$
$
£)r1(
£
$r1
UK
US
SF
FUS
SUK
SPOT-FORWARD PRICING (Underlying asset has cash payout)
• Continuous-time version
= instantaneous cash flow payout rate (e.g., dividend yield)
T)r(0T0
feSF
EXAMPLE: STOCK INDEX ARBITRAGE
• 8/5 S&P 500 index spot = 457.09 futures = 459.8 (12/16 delivery - 129 days from now)
• 129-day T-bill yield = 4.774%
• S&P div. yld. = 2.83%0282.
4
0283.1e
047337.r
))365/129(04774.1(e
4
f
129/365rf
STOCK INDEX ARBITRAGE (cont.)
80.459F
55.459
e09.457eS
T0
)365/129)(0282.047337(.T)r(0
f
CALENDAR SPREADS
• We have two futures contracts on the same asset but with different delivery dates, near (n) and far (f)
• How should the contracts be priced relative to one another?
)TT)(r(
T0
T0 nff
n
f eF
F
TWO INVESTMENT STRATEGIES(see Problem 7, Chapter 8)
State of the World
Strategy $/£ < 1.50 $/£ > 1.50
Lend £, Borrow$, Buy Put
1.50–1.50 = 0 $/£ - 1.50
Buy call 0 $/£ - 1.50
SAME PAYOFFS, SAME VALUE
2F
2US
S
2UK
2US
2UK
S
$
£)r1(
£
$)r1(
P)r1(
X
)r1(
£$
C
PUT-CALL INTEREST RATE PARITY
2US
2F
)r1(
X£$
PC