Financial Manager's Payoffs for Oil Prices
What are the payoffs per barrel for a financial manager who buys call options and sells put options on oil with an exercise price of $95 per barrel?
Given oil prices of $87, $92, $95, $98, and $103, what are the financial manager's payoffs per barrel?
Answer:
The financial manager's payoffs per barrel are -$8, $0, $0, $3, and $8 for oil prices of $87, $92, $95, $98, and $103, respectively.
A call option gives the buyer the right, but not the obligation, to buy a specified quantity of an underlying asset (in this case, oil) at a predetermined price (the exercise price) within a certain period of time. On the other hand, a put option gives the buyer the right, but not the obligation, to sell a specified quantity of the underlying asset at the exercise price within a certain period of time.
In this scenario, the financial manager buys call options and sells put options, both with an exercise price of $95 per barrel of oil.
If the oil price is below $95, the call option is out-of-the-money and will not be exercised. The financial manager's payoff per barrel for these prices would be $0.
If the oil price is equal to or above $95, the call option is in-the-money and can be exercised for a profit. However, since the financial manager sold a put option, they are obligated to buy oil at the exercise price of $95 per barrel if the price falls below $95.
For oil prices of $87, $92, $95, $98, and $103, the financial manager's payoffs per barrel would be calculated as follows:
- If oil price is $87: Call option payoff = $0, Put option payoff = -$8 (buying at $95 and selling at $87)
- If oil price is $92: Call option payoff = $0, Put option payoff = $0 (option not exercised)
- If oil price is $95: Call option payoff = $0, Put option payoff = $0 (option not exercised)
- If oil price is $98: Call option payoff = $3 (selling at $98 - $95 exercise price), Put option payoff = $0 (option not exercised)
- If oil price is $103: Call option payoff = $8 (selling at $103 - $95 exercise price), Put option payoff = $0 (option not exercised)
Therefore, the financial manager's payoffs per barrel are -$8, $0, $0, $3, and $8 for oil prices of $87, $92, $95, $98, and $103, respectively.