A 1-year European put option on a non-dividend paying stock has a strike price of 55. You are given: (i) The stock’s price is currently 50.

(ii) The stock’s price will be either 58 or 42 at the end of the year.

(iii) The continuously compounded risk-free rate is 3.75%.

The replicating portfolio consists of ∆ shares of stock and of lending B.

(a) Determine ∆ and B and calculate the put premium.

(b) Verify that the put price calculated in (a) is the same as if calculated using the risk-neutral pricing method.