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```Four ways to purchase a stock

Outright purchase
 Pay now:

𝑆0
Borrow to pay for the stock
 Pay later:

𝑆0 𝑒 𝛿𝑡
Prepaid forward contract
 Pay now:

𝑆0 − 𝑃𝑉(𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠)
Forward contract
 Pay in future:
Notes

Cost of carry
 Difference between interest and dividend rates
 Cost for you to borrow and buy stock, then hold it


Implied repo rate- interest rate used to find forward price
Cash and Carry
 Short a forward contract and buy the asset
 Pays off if forward price is too high
Futures contracts


Simply a standardized forward contract, sold in exchanges
Marked-to-market
 Changes in value are settled daily through parties
 Parties maintain margin accounts to cover these changes
Swaps


Simply a series of forward contracts
Payment
 Prepaid- pay now
 Postpaid- pay at end
 Level annual payments- most common

Types
 Commodity, eg. price of corn
 Interest rate
 Foreign currency
 Any of these could be deferred, or start in the future
Problem 1

The current price of a stock is \$84. A one-year forward contract
is entered into. It is expected that 4 quarterly dividends of \$5
each will be paid on the stock starting 3 months from now. The
4th dividend will be paid one day before expiration of the
forward contract. The risk-free interest rate is 6% compounded
quarterly. What is the price of a prepaid forward contract?
ASM p.612
Problem 2

A stock index pays dividends continuously at a constant rate of
5% per annum. The current price of one unit of the index is
\$50. What is the price of a prepaid forward contract for delivery
of one of the index in 3 months?
ASM p.612
Problem 3

A stock has a current price of \$65. A dividend of \$3.25 is
expected to be paid in 6 months. The risk-free interest rate is
10% effective per annum. X is the forward price of a one-year
forward contact that has the stock as the underlying asset.
Determine X.
ASM p.612
Problem 4

Suppose a stock index is currently priced at \$1,500, and the 12month forward price on that index is \$1,550. Let the annualized
dividend yield on the index be 2%, and let the continuously
compounded annual rate of (risk-free) interest be 8%. What
would the profit or loss at forward maturity (12 months from
now) under a cash-and-carry strategy?
ASM p.613
Problem 5



Take these forward prices for forward contracts of Stock ABC:
Years to Exp.
Forward Price
1
\$100
2
110
3
120
Take these spot rates of interest:
Term to maturity
Spot Rate
1
3.0%
2
3.5
3
3.8
X is the level swap price under a 3-year swap contract with the
same underlying asset. Determine X.
ASM p.630