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 45-strike put and sell two 40-strike puts both expiring in 91 days. That is, you enter into a put ratio spread. Both puts 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?