• Explain carefully the difference between hedging, speculation and arbitrage.
A trader is hedging when she has an exposure to the price of an asset and takes a position in a derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is betting on the future movements in the price of the asset. Arbitrage involves taking a position in two or more different markets to lock in a profit.
• Explain carefully the difference between selling a call option and buying a put option.
Selling a call option involves giving someone else the right to buy an asset from you. It gives a payoff of: – max(ST – K, 0) = min(K – ST, 0)
Buying a put option involves buying an option from someone else. It gives a payoff of: max(K – ST, 0)
In both cases the potential payoff is K – ST. When you write a call option, the payoff is negative or zero. (This is because the counterparty chooses whether to exercise.) When you buy a put option, the payoff is zero or positive. (This is because you choose whether to exercise.)
• When first issued, a stock provides funds for a company. Is the same true of a stock option? Discuss.
An exchange-traded stock option provides no funds for the company. It is a security sold by one investor to another. The company is not involved. By contrast, a stock when it is first issued is sold by the company to investors and does provide funds for the company.
• Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.
The holder of the option will gain if the price of the stock is above $52.50 in March. (This ignores the time value of money). The option will be exercised if the price of the stock is above $50.00 in March.
• A US company expects to have to pay 1 million Canadian dollars (CAD) in 6 months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.
The company could enter into a long forward contract to buy 1 million Canadian dollars in six months.
This would have the effect of locking in an exchange rate equal to the current forward exchange rate.
Alternatively, the company could buy a call option giving it the right (but not the obligation) to purchase 1 million Canadian dollars at a certain exchange rate in six months. This would provide insurance against a strong Canadian dollar in six months while still allowing the company to benefit from a weak Canadian dollar at that time.
• Delta hedging:
Suppose your position is long 10 call options (1 call = 100 shares) of MSFT
If the option delta is 0.25, how many shares should you buy or sell to be delta hedged?
Delta exposure is 0.25*10*100 = 250 shares long, so selling 250 shares is the hedge
• If you are long 50 put options on AAPL with an option delta of 0.85, how many shares should you buy or sell to be delta neutral ?
Delta exposure is -0.85*50*100 = 4250 shares, so buy 4250 shares to hedge