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8/10/2019 Forward Contracts slides

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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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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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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

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