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NEW QUESTION: 1
Which of the following relationships are true:
I. Delta of Put = Delta of Call - 1
II. Vega of Call = Vega of Put
III. Gamma of Call = Gamma of Put
IV. Theta of Put > Theta of Call
Assume dividends are zero.
A. I, II and III
B. I and III
C. II and IV
D. I, II, III and IV
Answer: D
Explanation:
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
