Çhapter 13: Options on Stock indices,
Currencies and Futures (Part II)
13.4 Currency Options
Foreign currencies are analogous to stocks
providing a known dividend yield (q) equal to the
risk free interest rate (rf) in the foreign country
Use the interest rate parity (see chapter 3)
F0 = S0 e(r-rf)T
To derive option pricing formules:
- replace q by rf
- replace S0 e-rf by F0 e-rT.
See: paragraph 13.8: (Black’s model for valuing
future options) formulas 13.17 and 13.18 are
equal to 13.11 and 13.12 where q = r.
13.5 Future Options
If a call futures option is exercised, the holder
acquires:
- a long position in the underlying futures contract
- a cash amount equal to the most recent
settlement future price – the strike price
If a put futures option is exercised, the holder
acquires:
- a short position in the underlying futures contract
- a cash amount equal to the strike price – the
most recent settlement future price
example 13.5
At August 15, an investor has a September futures
call option contract on copper with strike price of
70 cent per pound. One futures contract is on
25,000 pounds of copper
If the September futures price is currently 81 cents
and the close of trading on August 14 is 80 cents
If the option is exercised the investor receives
- 25.000 x (80 – 70 ) cent = $2500
- a long position in the underlying contract
(If the contract is closed he receives: $250)
Closing the contract leads to a total payoff:
$2750,- = (F - K) x 25000
Identical, but on August 15 an investor has an
September futures putoption contract with exercise
price of 100 cent per pound. One futures contract
is on 25,000 pounds of copper
If the September futures price is currently 81 cents
and the close of trading on August 14 is 80 cents
If the option is exercised the investor receives
- 25.000 x (100 – 80 ) cent = $5000
- a short position in the underlying contract
(If the contract is closed he must pay: $250)
Closing the contract leads to a total payoff:
$4750,- = (K - F) x 25000
Options on interest rate futures
At February the price of the June Eurodollars
contract is 93.82 (implicit three month Eurodollar
interest rate 6.18 % per annum)
The price of a call option on the contract with
expiration price 94.0 is 0.20.
When is this contract attractive? (By an expected
rise or an expected fall of the interest rate)
If the investor exercises the call option if the
interest rate has declined by 100 BP and the price
of the Eurodollar future contract is 94.82
The payoff is: 82 x $25
The cost of the contract: 20 x $25
The profit = 62x $25 = $1550
Reasons for popularity of futures contract
A futures contract is more liquid and easier to trade
than the underlying assets
A futures price is known immediately from trading
on the future exchange, whereas the spot price of
the underlying asset may not be so readily
available
[Before the trade on the New York stock exchange
starts, European stocks react on American futures]