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