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 z-score and 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 100 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)?