Mr. Black has been asked by a client to write a large put option on the S&P 50

Mr. Black has been asked by a client to write a large put option on the S&P 500 index. The option has an exercise price and a maturity that are not
available for options traded on exchanges. He therefore has to hedge the position dynamically. which of the following statements about the risk of his
position are not correct?

a. He can make his portfolio delta neutral by shorting index futures contracts.

b. There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.

c. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written.

d. To make his hedged portfolio gamma natural. He needs to take positions in options as well as futures.