Explanation:
All the statements are correct, and represent the relationships between the values of the Greek variables for calls and puts for the same option. It is important to know why as the PRM exam often asks tough questions about the Greeks.
Statement I is correct because of the put-call parity. According to the put-call parity,
Value of call - Value of put = Spot price - Exercise price discounted to the present
Now the delta of the spot is 1, and that of the discounted price is zero. Therefore
Delta of Call - Delta of Put = 1 - 0, or by rearranging we get the equation in statement I.
Statements II and III are correct as the gamma and vega of both the spot price and the discounted price are zero. Therefore using the put-call parity, we can say
Gamma of Call - Gamma of Put = 0 - 0, and
Vega of Call - Vega of Put = 0 - 0
Rearranging, we get statements II and III.
Statement IV is correct because of the following relationship between theta of call and theta of put:
Theta of Put = Theta of Call + rKe^(-rt).
Since rKe^(-rt) can only be a positive number, theta of put can only exceed the theta of a call. However, since theta is generally negative, it often implies that the theta of a call is the larger absolute number.
Additional explanation for the last point: Assume rKe^(-rt) =+1 and theta of a put is -5 (completely hypothetical)
Now Theta of Put = Theta of Call + rKe^(-rt)
Ie -5 = -6 + 1
Now -5 is the larger number than -6. In other words, theta of put exceeds that of the call in a pure mathematical sense, which is what I mean when I say “theta of put can only exceed the theta of call”. But if you ignore the sign, then theta of call is larger at 6 when compared to 5. Therefore the theta of the put is greater than the theta of the call – which is what the answer says.
