1. You are considering entering one of the following positions, all on the same underlying non- dividend-paying stock, and all with the same amount of time to expiry: (1) short an at-the- money straddle; (2) short a deep-in-the-money put; (3) short a deep-out-of-the-money call; (4) long a strangle; (5) long a bearish put spread consisting of a combination of an in-the-money put and an out-of-the-money put; (6) short an at-the-money call.

   1. (a) In the Black-Scholes model, which position would definitely have a positive delta? (No justification is needed: simply write down a number from 1 to 6, and do the same for the next five parts.)

   2. (b) Which would have the largest (most positive) gamma?

   3. (c) Which could have either a positive or negative gamma?

   4. (d) Which would have the largest (most positive) theta?

   5. (e) Which would perform best if implied volatility suddenly declined?