Option pricing under lognormal distribution. ON 12/17/2021 Friday, SPX currently trades at 4620. March put has 3 months (63 trading days) to expiration. March 4275 strike PUT currently trades at 25% implied volatility. Assuming risk free rate of zero.

Q1a. What is the probability that the put will expire in the money (5 points)?

Q1b. What is the average underlying spx price when put expires ITM (5 points)?

Q1c. What is the average put payment conditional on put expiring ITM? (5 points)

Q1c. How much should the put be priced at today? (5 points)