Q3. Consider the following data: S = 100; r = .08; s = .3 on the following two options:

Call 1 Call 2

K = 100; K = 90

T-t=90 days. T-t=180 days.

Price: 6.91 16.33

Delta: .58 .78

Gamma: .02 .0138

3.1 A trader just shorted 100 CBOE calls 2.

Calculate the number of shares necessary to create a Delta Neutral position.

3.2 A trader just shorted 100 CBOE calls 2.

Calculate the number of calls 1 and shares of the underlying stock that the trader must hold (long or short) in order to create a Delta-Gamma neutral position

Q4. A trader just shorted 100 of calls 1 and 100 of calls 2 from Q3.

Calculate the delta and the Gamma of this position.

Q5. Consider put 1 and put 2, which are on the same stock and with the same exercise prices and time to expiration as their respective calls from Q3.

Calculate the number of shares covered in put 1 that together with the short calls 1 and 2 from Q3. create a Delta-neutral position.

Q6. Calculate the number of the shares in put 1 and put 2 needed to create a delta-Gamma neutral portfolio consisting of the short calls (call 1 and call 2 from Q3.) and the two puts.