Question

Consider two calls with the same time to expiration that are written on the same underlying stock. Call One trades for $7 with a strike price of $100. Call Two has an exercise price of $95. What is the maximum price that Call Two can have? Use the potential arbitrage profits to critically explain your answer.

Answer 1

Answer-

A no-arbitrage condition places an upper bound on the value of Call 2. The price of Call 2 cannot exceed the price of the option with the higher exercise price plus the $5 difference in the two exercise prices. Thus, the upper bound for the value of Call 2 is $12. If Call 2 is priced above $12, say, at $13, the following arbitrage becomes available.

Sell Call 2 for cash flow $13 and buy Call 1 for cash flow $7. This is a net cash inflow of $6. If Call 2 is exercised against you, you can immediately exercise Call 1. This provides the stock to meet the exercise of Call 1 against you. On the double exercise, you receive $95 and pay $100, for a net cash flow of $5. However, you received $6 at the time of trading for a net profit of $1. This is the worst case outcome