Q1. You believe stock price by year end will have the following multinomial distribution:

Price Probability 50 5% 75 20% 100 50% 125 20% 150 5% Q1a. What should be the stock price TODAY?

Q1b. what is the prob that a 110 strike PUT will expire ITM?

Q1c. what is the conditional average price of underlying stock when 110 strike PUT expires ITM?

Q1d. what is the conditional average payment from the 110 strike PUT option when the PUT expires ITM?

Q1e. based on Q1b-Q1d, how much should the 110 PUT be priced at today?

Q1f. Out of the total value of the put from Q1e, how much is intrinsic value and how much is time value?

Please, show a work