2. (18 points) The following table represents the true probabilities, the risk-neutral probabilities and the price distribution for an underlying stock 6 months from now. Show your calculations. Probs p RNPs a ST 1.00 1.00 .04 .08 50 .16 .18 60 33 .34 70 27 26 80 20 .14 90 a) What is the true expected value of the stock price in 6 months? b) What is the certainty equivalent of the stock price in 6 months? c) If there are no arbitrage opportunities in the forward market, what must be the stock's 6-month forward price? d) If the options are European and subject to stock-type settlement, and if the simple interest rate is 8% per year, what is the certainty equivalent in 6 months of a call with a $75 strike and 6-month expiry? What is its current theoretical value? e) Under the same conditions, what are the 6-month certainty equivalent and current theoretical value of a put with a $75 strike and 6-month expiry? f) Show that Put-Call Parity holds. 2. (18 points) The following table represents the true probabilities, the risk-neutral probabilities and the price distribution for an underlying stock 6 months from now. Show your calculations. Probs p RNPs a ST 1.00 1.00 .04 .08 50 .16 .18 60 33 .34 70 27 26 80 20 .14 90 a) What is the true expected value of the stock price in 6 months? b) What is the certainty equivalent of the stock price in 6 months? c) If there are no arbitrage opportunities in the forward market, what must be the stock's 6-month forward price? d) If the options are European and subject to stock-type settlement, and if the simple interest rate is 8% per year, what is the certainty equivalent in 6 months of a call with a $75 strike and 6-month expiry? What is its current theoretical value? e) Under the same conditions, what are the 6-month certainty equivalent and current theoretical value of a put with a $75 strike and 6-month expiry? f) Show that Put-Call Parity holds