A call option with a $1.75 premium has a delta of 0.7 and 30 days to maturity. A dealer sells 100 contracts (=10,000 calls), and wants to delta hedge by purchasing X shares of the stock at $100 per share. Show work.
a) Calculate X
b) Calculate the initial value of the portfolio
c) Calculate the portfolio value a day later if the stock price remains at $100 and the call price drops to $1.70.