Question

A one-month European call option on a non-dividend-paying stock is currently selling for$2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?

Answer 1

First we will calculate the present value of strike price:

50e^-0.06*1/12 = 49.75

As 2.5<49.75-47, an arbitrgeur should borrow $49.50 at 6% for on month, buy the stock and buy the put option. This position will help in generating the profit. If the stock price goes above $50 in one month, th option expires worthless, but the stock can be sold for atlest $50. As the present value of $50 is $49.75, therefore the strategy will generate the profit of $0.25

If the stock price goes below $50, the put option is exercised and profit will be generated of $0.25.