The current stock price of a non-dividend paying stock S is $100 and interest rate is 5% per annum.

3. The current stock price of a non-dividend paying stock S is $100 and interest rate is 5% per annum. An option trader has long a European call on 50,000 shares of the stock S. The maturity of the option is 5 months and strike price is $110. The implied volatility is 30% per annum. He wants to hedge out the gamma exposure, and the available option from the market is 6 months at the money call. i) Find out the amount of 6Months At Time Money (ATM) call that he has to long/short to keep the portfolio gamma neutral. ii) After he has long/short the 6 Months ATM call, how many shares he has to buy/sell to keep the total portfolio delta neutral