What should the trader do?

A trader comes in to work and finds the following prices in relation to a stock: $100 spot, $10 for a call expiring in one year with a strike price of $100, and $10 for a put with the same expiry and strike. Interest rates are at 5% per year, and the stock does not pay any dividends.

What should the trader do?
A . Buy the call, buy the put and sell the stock
B . Buy the call, sell the put and sell the stock
C . Buy the put, sell the call and buy the stock
D . Do nothing

View Answer

Answer: B

Explanation:

The prices must satisfy the put-call parity, and if they do not, it means there is an arbitrage opportunity, The put-call parity is as follows. We plug in the values to check if the parity is maintainted.

Buying a call + Bank Deposit (PV of exercise price) = Buying the stock + Buying a put Thus the LHS = $10 + $100/(1 + 5%) = $105.24 and RHS = $100 + $10 = $110, ie the equality does not hold.

Since the trader can make a profit by buying low and selling high, and the set of positions on the left should be brought, and those on the RHS should be sold. Thus the trader should buy the call, sell the put and sell the stock to make a risk free profit. (There is no need to explicitly place a bank deposit at the risk-free rate).