The current price of a non-dividend-paying stock is $40. Over the next six months it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. The risk-free interest rate is 2% per annum with continuous compounding.

What position would the investor need to take in the stock to hedge this position?

What is the value of each option using no-arbitrage arguments?