Use the following data from 2023-02-13 for a group of Sep $405 options on futures contracts

Current futures price: $401 Expiration: 2024-09-27 Risk-free rate: 8% (discrete) Call market price: $14.2 Put market price: $9.35 Assume a standard deviation of 14% and use the Black 76 model to determine if the options are correctly priced. Note: The table of cumulative normal distribution is on the Moodle site. If you are using Excel, you need to round dkdk to 2 digits and N(dk)Ndk to 4 digits.

a. What is the value of d1d1? 0.03 Round your answer to two decimal places.

b. Determine whether the put-call parity holds

No, because the PCP put price $17.73 is larger than the market put price $9.35.

No, because the PCP put price $7.48 is smaller than the market put price $9.35.

No, because the PCP put price $14.025 is larger than the market put price $9.35.

c. What is the theoretical value of the call option? $ Round your answer to two decimal places.

d. What is the theoretical value of the put option? $