Consider a European put option on a stock with strike $35 and maturity 9 months. The stock price is currently $34, the volatility of the stock price is 0.21 and the continuously compounded risk-free interest rate is 6% per annum.

(i) Compute the delta, the gamma and the vega of a short position in 50 European put options on the stock. Discuss any reason for gamma hedge.

(ii) If the stock price decreases to $33.10 the next day, find the profit/loss on the options position and the new delta of the options position in part (i).