8006 Exam Dumps : Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

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.

The stock has a beta of 1.2, therefore intuitively it can be expected to earn more than the broad market index. It will earn the risk free rate, ie 3%, and 1.2 times the equity risk premium of 5% (8% - 3%). The expected returns from the stock therefore are 3% + (8% - 3%)*1.2 = 9%

The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x - y)^2 for x > y; and -(x - y)^2 for x < y.

For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative. For this question, let us calculate the second derivative and see what the gamma is:

If x > y, then the payoff is (x - y)^2

The first derivative wrt x is 2(x - y)

The second derivative wrt x is 2.

ie, the gamma is 2

If x < y, then the payoff is -(x - y)^2

The first derivative wrt x is -2(x - y)

The second derivative wrt x is -2.

ie, the gamma is -2

If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.

Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and therefore Choice 'b' is the correct answer.