Show detailed work.

A stock has a price of $40. The risk-free interest rate is 7% per annum and the stock has volatility parameter of 28%. Consider a European call option on the stock for a strike price of $41 with expiration in 6 months. Let t be the current time and t + h an hour later.

a. From time t to t + h, the price of the stock increases by 1%. What is the percentage change in the value of the call? Would the price of the put move by the same percentage?

b. From time t to t + h, the price of the stock decreases by 1%. What is the percentage change in the value of the call? Would the price of the put move by the same percentage?