A stock is currently trading for $40 per share. The stock will pay no dividends. The annual continuously compounded risk-free interest rate is 0.08, and the stock price volatility is 0.3. Suppose you buy a 40-strike call and sell a 45-strike call both expiring in 91 days. Both calls are written on 100 shares.
(a) What investment is required for a delta-hedged portfolio?
(b) What is your profit the next day if the stock falls to $39?
(c) What if the stock goes up to $40.50 instead?
(d) Now assuming stock price volatility is 0.25. Suppose you sell a 60-strike call expiring in 91 days. What is the overnight profit if the stock goes up to $60.35?