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Forward Contracts
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Definition
forward contract is an agreement between two parties in which one party, the
buyer; agrees to buy from the other party, the seller; an underlying asset or
other derivative, at a future date at a price established at the start of the
contract.
The buyer is often called the long.
Seller is often called the short
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Important Characteristics of the forward
contracts
No money changes hands at the start of the contract
Delivery and Settlement of a forward contract
Delivery (Deliverable forward contracts)
Cash settlement (NDFs)
Default Risk
Termination of the contract
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Structure of global forward markets
Part of vast network of financial institutions
Some specializes in certain markets & contracts
Parties in contracts
End users (corporations, non profit organization, government) Dealers (Brokers)
Transactions in forward markets are on phone
Credit risk
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Types of Forward contracts
Equity Forward contracts Forward contracts on Individual stocks
Forward contracts on stock portfolio
Forward contracts on stock indices
Bond and interest rate forward contracts Forward contracts on Individual bonds
Forward contracts on bond portfolio
Forward contracts on bond indices
Forward rate agreements (FRAs)
Currency Forward contracts
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Forward rate agreements (FRAs)
Consider an FRA expiring in 90 days for which the underlying is 180-day LIBOR.
Suppose the dealer quotes this instrument at a rate of 5.5 percent and notional
principal is $10 million. Suppose that at expiration in 90 days, the rate on 180-day
LIBOR is 6 percent.
Present value of this amount would be
At expiration party going long will receive
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Forward rate agreements (FRAs)
FRA payoff formula in general is
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FRA Descriptive Notation and Interpretation
Off the run forward contracts (non- standardized)
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Currency Forward contracts
Emerge in 1970s
Users (banks and corporations)
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Other types of forward contracts
Commodity forwards
Energy Forwards
Weather forwards
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PRICING AND VALUATION OF FORWARD CONTRACTS
Price is the fixed price or rate at which the transaction scheduled to occur at
expiration will take place. This price is agreed to on the contract initiation date and
is commonly called the forward price or forward rate. Pricing means to determine
the forward price or forward rate.
Valuation, however, means to determine the amount of money that one would need
to pay or would expect to receive to engage in the transaction.
GENERIC PRICING AND VALUATION OF FORWARD CONTRACTS
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Notations for Pricing and Valuation
So = price of the underlying asset in the spot market at time 0,
St = price of the underlying asset in the spot market at time t,
ST at time T.
F(0,T) = forward contract price at time 0
Vo(O,T) = value of the forward contract at time 0
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Valuation of forward contracts
At expiration
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Pricing a forward contract
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Valuing a forward contract
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Pricing and Valuation Formulas for a Forward Contract
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Pricing and Valuation of Equity Forward Contracts
Many stocks pay dividends during the life of contracts so their effect should be
adjusted.
Suppose if there is a stream of dividends that would be received during the life of
contract is that will occur at then there present value would
be
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Continued
And we know that in the absence of arbitrage opportunity
So if dividend adjustment is required then forward price would be
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Example
Consider a stock priced at $40, which pays a dividend of $3 in 50 days. The risk-
free rate is 6 percent. A forward contract expiring in six months (T = 0.5) would
have a price of
Suppose if risk-free rate is 4 percent. The forward contract expires in 300 days and
is on a stock currently priced at $35, which pays quarterly dividends according to
the following schedule:
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Continued
Another approach can be through future value of dividends
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Continued
Suppose if dividends are considered to be paid continuously then formula can be
derived by first converting the discrete risk free rate r into the continuously
compounded rate
Then Forward price would be
where = Continuously compounded dividend yield rate
= exponent for continuous compounding
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Example
Consider a forward contract on France's CAC 40 Index. The index is at 5475, the
continuously compounded dividend yield is 1.5 percent, and the continuously
compounded risk-free interest rate is 4.625 percent. The contract life is two years.
With T = 2, the contract price is, therefore,
Similarly dividends adjustments can also be done while doing valuation so
for valuation
and in case of continuous compounding valuation would be
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Pricing and valuation of fixed income and
interest rate forward contracts
Alternatively
The value of the forward contract at time t would be
And at maturity value would be
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Example Consider a bond with semiannual coupons. The bond has a current maturity of 583 days and
pays four coupons, each six months apart. The next coupon occurs in 37 days, followed bycoupons in 219 days, 401 days, and 583 days, at which time the principal is repaid. Suppose
that the bond price, which includes accrued interest, is $984.45 for a $1,000 par, 4 percent
coupon bond. The coupon rate implies that each coupon is $20. The risk-free interest rate is
5.75 percent. Assume that the forward contract expires in 310 days. The present value of the
coupons is
Now assume it is 15 days later and the new bond price is $973.14. Let the risk-free interest
rate now be 6.75 percent. The present value of the remaining coupons is
Value of the forward Contract would be
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Pricing and valuation of FRAs
Payoff on the FRA can be found by multiplying the notional amount with the following
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Example
Consider a 3 X 9 FRA. This instrument expires in 90 days and is based on 180-day
LIBOR. Thus, the Eurodollar deposit on which the underlying rate is based beginsin 90 days and matures in 270 days.Today is day 0, h = 90, m = 180, and h + m =
270. If current rates are
Value of the forward contract at time g would be
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Continued.
Assume that we go long the FRA, and it is 25 days later. We need to assign a value
to the FRA First note that g = 25,h - g = 90 - 25 = 65,andh+ m - g = 90 + 180 - 25 =
245. Let the rates are
Then value of the FRA would be