Need help with solving rhesw with explaninatio

You are a trader in S\&P 500 Index options for an investment bank. Your position has the following net greeks (after multiplying the position size times the gamma per exercise price and the price multiplier): delta =0, gamma =$400. The S\&P 500 Index is currently at $2665. (1) if the S\&P 500 Index moves to \$2664 what is the new net delta of the position? (show work) a. it's still zero b. $400 c. +$400 d. $800 e. +$800 f. none of the above (2) given your answer in 13(1), above, what offsetting transaction would you do to dynamically hedge the delta? a. buy 400 shares of the S\&P 500 Index b. sell 800 shares of the S\&P 500 Index c. sell 400 shares of the S\&P 500 Index d. nothing because the position is already delta-neutral e. buy 800 shares of the S\&P 500 Index