Suppose that call options on XYZ stock with time to expiration $3$ months and strike price $$90$ are selling at an implied volatility of $30\%.$ ExxonMobil stock price is $$90$ per share, and the risk$-$free rate is $4\%.$

Required:

a$1-$ If you believe the true volatility of the stock is $32\%,$ would you want to buy or sell call options?

a$2-$Now you want to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?