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.
(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
(b) Which would have the
largest (most positive) gamma?
(c) Which could have
either a positive or negative gamma?
(d) Which would have the
largest (most positive) theta?
(e) Which would perform
best if implied volatility suddenly declined?