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# Derivatives-delta, gamma, theta of options, delta neutrality

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1. Given the following information is given to you: T= 100 days, r = 5%, S = \$45, and standard deviation = 0.26, calculate the delta of a \$45 Call. How do you interpret this delta?

2. Consider a European call with the following details:

Stock price = \$17.50
Strike price = \$17.00
r = 0.08
Variance = 0.10
T = 0.25

a) Compute the delta for this call and explain as much as you can about this delta value.
b) Compute theta for this call.
c) Compute gamma for this call.
d) What is the meaning of delta neutrality?

3. For a 350 call and a 360 call, following table is given:

Option Delta Gamma Theta

350 call 0.709 0.01 -0.093
360 call 0.599 0.011 -0.103

Suppose you buy 25 of 350 calls and write 25 of 360 calls.

a) What is your position delta?
b) What is your position gamma?
c) What is your position theta?

4. A portfolio contains 125 contracts of XYZ JUN 50 call options (European style), which sell for \$3 and have a delta of 0.520. How many JUN 50 puts must you buy to be approximately delta neutral?

5. A portfolio contains 2,500 shares of ABC common stock and the following information is given to you:

Option Price Delta Theta

JUL 40 call 1.75 0.534 0.03
JUL 35 put 0.875 -0.312 0.02

You decide to write the JUL 40 calls and buy the JUL 35 puts so as to be approximately delta neutral and have no cash flow. How many of each option would you buy or write?