30 Two-state Option Pricing Model Maverick Manufacturing plc must purchase gold in three months for use in its operations. Maverick’s management has estimated that if the price of gold were to rise above

$875 per ounce, the firm would go bankrupt. The current price of gold is $850 per ounce. The firm’s chief financial officer believes that the price of gold will either rise to $900 per ounce or fall to $825 per ounce over the next three months. Management wishes to eliminate any risk of the firm going bankrupt. Maverick can borrow and lend at the risk-free APR of 16.99 per cent.

(a) Should the company buy a call option or a put option on gold? To avoid bankruptcy, what strike price and time to expiration would the company like this option to have?

(b) How much should such an option sell for in the open market?

(c) If no options currently trade on gold, is there a way for the company to create a synthetic option with identical payoffs to the option just described? If there is, how would the firm do it?

(d) How much does the synthetic option cost? Is this greater than, less than or equal to what the actual option costs? Does this make sense?