Assume, S = 100, r = 10% pa (continuously compounded), K = 100, = 20% pa and a put option has 6-months to maturity.

(i) Use the Black-Scholes formula to price a European put option (P) on a (nondividend paying) stock and calculate the delta. Show values for d1, d2, N(d1), N(d2) and P. Explain if and why the Black-Scholes price gives the correct options price.

(ii) Explain intuitively, what happens to the put premium if next day, volatility increases to = 30%pa. Calculate the vega of the put. Explain if and how you would vega-hedge your options position and whether this results in zero risk for your put option