Question

1. 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

Maximum Price that Call Two can have = Price of Call One + Difference between the Strike Prices = 7 + (100-95) = 7+5 = $12

If the Price of Call Two is more than $12, lets say, $13. In that case, there is an Arbitrage Opportunity as follows:

We can Sell the Call with $95 Strike and Buy the Call with $100 Strike. In that position, maximum loss will occur, if Stock Price is more than $100.

Maximum Loss will be = Difference between Strike Price + Net Premium Received = (Option Sold-Option Bought)+(Premium Received on Selling-Premium Paid on Buying) = (95-100)+(13-7) = -5+6 = Profit of $1

Therefore, if Price of Call Two is more than $12, there will NO LOSS in any situation. There will be an Arbitrage Profit.