A one-month European option on a non-dividend-paying stock is currently selling

Question

A one-month European 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?
(I don’t understand why the arbitrageur should borrow $49.50 at 6% for one month, buy the stock, and buy the put option. How to come up with this strategy?) A one-month European 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?
(I don’t understand why the arbitrageur should borrow $49.50 at 6% for one month, buy the stock, and buy the put option. How to come up with this strategy?)
(I don’t understand why the arbitrageur should borrow $49.50 at 6% for one month, buy the stock, and buy the put option. How to come up with this strategy?)

Explanation / Answer

Put option is an option to sell. A put option buyer can sell the stock in 1 month at $50.

Monthly interest rate is 0.50% (6%÷12)

Value of investment with interest after 1 month:

= ($47+$2.50)×(1+0.50%)

= $49.50×1.005

= $49.75

Hence, arbitrage profit is $0.25 per share ($50-$49.75)

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