you are making a market in nat gas options. on 27 march 2024 you sold put options on 100 july, 2024 natural gas futures contracts. the options are struck at $2.10 MMBTU. The relevant volatility is 43.52 percent, and the relevant interest rate is 5 percent. the options expire on 25 june 2024. the current july 2024 NG futures price is $2.285/MMBTU. each contract is for 10000 MMBTU. A) what is the price of the options sold? B) what are the gamma, delta and vega of the entire position in the options you sold? C) what are the risks associated with this transaction? D) Devise a delta hedge for this transaction. How many futures contracts should you trade? forr what delivery month? should you buy or sell? E) what risks do you face when you merely delta hedge? how can you mitigate these risks? F) you have an opportunity to purchase calls on july 24 NG struck at $2.5/MMBTU. devise a transaction in the $2.5 stike july 24 calls and july 24 futures that offsets the delta and gamma risks of your original sale of puts. How many 2.5 calls should you trade? should you buy or sell? how many