Question

The price of a non-dividend-paying stock is $35. The risk-free interest rate is 8% based on continuous compounding. The price of a European put on the stock is $3. Assume the strike price is $40, and the expiration date is in 5 months. Based on the information above, is there any arbitrage opportunity? And if there is, what profit might a trader capture?

Answer 1

Arbitrage opportunity (if available) can be leveraged by following the steps given below:

- Borrow $ 35 to purchase the stock and another $ 3 to purchase the put option on the stock at present time.

- The borrowings would lead to a total borrowing liability of (35+3) x EXP[0.08 x (5/12)] where 8 % is the continuously compounded risk-free rate and 5 months is the option tenure.

- Borrowing Liability after 5 months = (35+3) x EXP[0.08 x (5/12)] = $ 39.288

- Under the put option terms, the stock will be sold at the strike price of $ 40 irrespective of the actual stock price at option maturity.

- Arbitrage Profit (Risk-less) = 40 - 39.288 = $ 0.712

The above steps show that the investor can generate riskless (arbitrage) profit by borrowing the money for the stock and the put option, followed by exercising the option to sell the stock at the put's strike price.