Practice Questions:
1.15 It is May and a trader writes a September call option with a strike price of $20. The
stock price is $18 and the option price is $2. Describe the trader’s cash flows if the option is
held until September and the stock price is $25 at this time.
The trader's cash inflows were $2 in May, and $2 was cash from the sale of options. In
September, cash outflows were $5, and $5 was the result of exercising options. Investors must
buy stocks for $25 in September and then sell them to option buyers for $20.
1.16 An investor writes a December put option with a strike price of $30. The price of the
option is $4. Under what circumstances does the investor make a gain?
If the price of the stock is higher than $26 when it is exercised, the trader will make a gain.
1.18 An airline executive has argued: ‘‘There is no point in our using oil futures. There is
just as much chance that the price of oil in the future will be less than the futures price as
there is that it will be greater than this price.’’ Discuss the executive’s viewpoint.
Oil futures are used to invest in value preservation. It is more important for airlines. It is
equivalent to an insurance on an airline. When oil prices rise, it can avoid risks and reduce the
operating costs of enterprises. When oil prices fall, we can not Holding oil positions, thereby
expanding corporate profits. A large part of the operating cost of airlines comes from oil, which
means that the oil price can directly affect their profitability. Especially when the oil price rises,
airlines may run at a loss. At this time, companies can selectively buy some oil futures to offset
this risk.
1.19 Options and futures are zero-sum games.’’ What do you think is meant by this
statement?
This statement means that the gain (loss) of short positions on options and futures is the loss
(gain) of long positions. The sum of their gain-losses is zero.
1.20 A trader enters into a short forward contract on 100 million yen. The forward
exchange rate is $0.0080 per yen. How much does the trader gain or lose if the exchange
rate at the end of the contract is (a) $0.0074 per yen; (b) $0.0091 per yen?
(a) Gain = 100× (0.0080-0.0074) =0.06 millions of dollars =$60,000
(b) Loss = 100× (0.0091-0.0080) =0.11 millions of dollars =$110,000
1.21 A trader enters into a short cotton futures contract when the futures price is 50 cents
per pound. The contract is for the delivery of 50,000 pounds. How much does the trader
gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b)
51.30 cents per pound?
(a) Gain = ($0.5000-$0.4820) ×50,000 =$900
(b) Loss = ($0.5130-$0.5000) ×50,000 =$650
Further Questions:
1.28 On May 13, 2015, as indicated in Table 1.2, the spot offer price of Google stock is
$532.34 and the offer price of a call option with a strike price of $525 and a maturity date
of September is $30.40. A trader is considering two alternatives: buy 100 shares of the
stock and buy 100 September call options. For each alternative, what is (a) the upfront cost,
(b) the total gain if the stock price in September is $600, and (c) the total loss if the stock
price in September is $500. Assume that the option is not exercised before September and if
stock is purchased it is sold in September.
(a) The upfront cost for stock alternative is $532.34×100 =$53,234
The upfront cost for option alternative is $30.30×100 =$3,040
(b) The gain from the stock alternative is $600×100-$53,234 =$6,766
The total gain from the option alternative is ($600-$525) ×100-$3,040 =$4,460
(c) The loss from the stock alternative is $53,234-$500×100 =$3,234
The total loss from the option alternative is $3,040
1.29. What is arbitrage? Explain the arbitrage opportunity when the price of a dually listed
mining company stock is $50 (USD) on the New York Stock Exchange and $60 (CAD) on
the Toronto Stock Exchange. Assume that the exchange rate is such that 1 USD equals 1.18
CAD. Explain what is likely to happen to prices as traders take advantage of this
opportunity.
Arbitrage involves locking in a riskless profit by simultaneously entering into transactions in two
or more markets. Traders can buy stocks on the NYSE and then sell them on TSE, thus locking
in profits of 60/1.18-50 =0.847 per share. When traders take advantage of this opportunity, the
price of the NYSE will rise, and the price of the Toronto Stock Exchange will fall.
1.31 A U.S. company knows it will have to pay 3 million euros in three months. The current
exchange rate is 1.1500 dollars per euro. Discuss how forward and options contracts can be
used by the company to hedge its exposure.
In terms of forward contracts, the company can sign a forward contract that requires it to
purchase 3 million euros at a forward price within three months. The forward price will be close
to the same current spot price of 1.1500. From the perspective of an option contract, a call option
needs to be purchased, giving the company the right to buy 3 million euros at the strike price
within three months. The use of forward contracts can lock in the exchange rate after 3 months.
The use of a call option provides insurance at a certain cost for the exchange rate to be higher
than the strike price.
1.33 The price of gold is currently $1,200 per ounce. Forward contracts are available to buy
or sell gold at $1,400 per ounce for delivery in one year. An arbitrageur can borrow money
at 5% per annum. What should the arbitrageur do? Assume that the cost of storing gold is
zero and that gold provides no income.
Arbitrage should borrow money to purchase a certain amount of current gold and sign a one-year
forward contract. This way gold will be bought at $1,200 per ounce and sold for $1,400 per
ounce. Since the interest rate is 5%, the interest is 0.05×$1,200= $60 per ounce. So, the profit is
($1,400-$1,200)-$60= $140.