Assume rf = 0 for all questions below.

Underling at 100. Annual stdev of $20. 3 months left for the option.

Q1. Pricing Under Normal Distribution. PUT has a strike of90.

Q1a. What is the z-score for PUT strike?

Q1b. What is the probability for PUT to expire in the money?

Q1c. What is the average price of the underlying at expiration conditional on PUT expiring ITM?

Q1d. What is the average payment of the option conditional on expiring ITM?

Q1e. How much should the 90 strike PUT be priced at?

(for additional practice price a 90 CALL, 110 CALL, and 110 PUT)

Q2. Delta and Gamma.

Q2a. What is the delta of 110-90 put debit spread (long 110 strike put and short 90 put)?

Q2b. What is the gamma value of a 90-110 call debit spread (long 90 call and short 110 call)?

Q3. You want to construct a delta-neutral CALL front ratio spread. Long 1x ATM 50 delta CALL, and short 2x 25 delta OTM Call. What strike call will give you a 25 delta? What is the gamma value of the spread?

Q4. You want to construct a PUT back ratio spread. Long 2 x 25 delta OTM PUT, and short 1x 50 delta ATM PUT. What strikes are the PUT options you are using? What is the gamma value of the spread?

Q5. Gamma vs. theta

You short an ATM straddle, ie 1x ATM CALL + 1x ATM PUT.

Q5a. What is the gamma and delta value of the position?

Q5b. How much theta are you paying or collecting each day?

Q5c. Underlying moved down by $5 in a single day. How much should the price move based on

i. delta; ii gamma; iii. theta