A stock is trading at $60 and has an annual volatility of 25%. The risk-free interest rate is 2%. A 3-month European put has a strike price of $55. (1) What is the delta of the put? If stock price increases to $61, what is the approximate change to the value of the put based on delta? (2) What is the theta of the put? In one trading day, what is the approximate change to the value of the put based on theta? (3) What is the rho of the put? If the Fed cuts interest rate by 0.5% today, what is the approximate change to the value of the put based on rho? (4) What is the vega of the put? Intuitively, why is vega positive? (5) If you have sold the put, how do you fully hedge your position with stock and bond?

Please show work in excel. Thanks