Question

Please show work.

The following are three-month call option prices: the call at strike 100 is trading at $ 5 and the call at strike 102 is trading at $ 2.5. The rate of interest (continuously compounded) is 3%. Is there an arbitrage strategy is this market and how would you implement it? Draw a cash flow table showing the outcome of your strategy at maturity for every possible stock price level.

Answer 1

Option 1: Premium = $ 5 and Strike Price = $ 100

Option 2: Premium = $ 2.5 and Strike Price = $ 102

The arbitrage strategy would involve selling Option 1 and buying Option 2.

Initial Cash Flow:

Option 1 Sold = $ 5 and Option 2 Bought = - $ 2.5

Net Initial Cash Flow = 5 - 2.5 = $ 2.5

This net inital cash flow can be invested at the continuously compouned interest rate of 3 % for 3 months to yield [2.5 x e^(0.03 x0.25)] = $ 2.5188

The cash flow table for every price level would be as given below: