You just bought $1,000,000 worth of puts on IBM with delta -0.5. You delta-hedged immediately with IBM stock. Everything else being equal, which of the following is correct?

a. The value of your portfolio will fall if the implied volatility of IBM suddenly increases.

b. The value of your portfolio will increase if the implied volatility of IBM suddenly increases.

c. The value of your portfolio will remain the same if the implied volatility of IBM suddenly increases.

d. Within the Black and Sholes framework, the portfolio value will fall when the IBM stock price goes up.

e. Within the Black and Sholes framework, the portfolio value will fall when the IBM stock price goes down.

f. None of the above is correct