Question

A one-month European call option on a non-dividend-paying stock is currently selling for$2.50. The stock price is $45, the strike price is $50, and the risk-free interest rate is 5% per annum. What opportunities are there for an arbitrageur?

Answer 1

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Answer:

In this case the present value of the strike price is 50e^-0.06*12 = 49.75

Because. 2.5 < 49.75 - 45

An arbitrageur should borrow $47.5 ( 45+2.5) at 6% for one month, buy the stock, and buy the put option. This generates a profit in all circumstances.If the stock price is above $50 in one month, the option expires worthless, but the stock can be sold for at least $50. A sum of $50 received in one month has a present value of $49.75 today. The strategy therefore generates profit with a present value of at least $2.25 (49.75 - 47.5).. If the stock price is below $50 in one month the put option is exercised and the stock owned is sold for exactly $50 (or $49.75 in present value terms). The trading strategy therefore generates a profit of exactly $2.25 in present value terms.