You have been tasked with modeling and finding the price of a call option on a "market basket" of three assets... (See picture below, please do all parts, Thank you :))

i,T 3. You have been tasked with modeling and finding the price of a call option on a "market basket" of three assets. The option pays out max(0,(Y, K)) where Y, = 9,S1,1 +9292,7+q;$3,1, 9; is a portfolio weight, and S; is the stock price for stock i= 1, 2, and 3 at the end of day T. On day t= 0 (today) you observe the current stock prices (S.,0,S2,09930) and have estimated the mean drift rates Mi; and volatilities o, for each stock i. You have also estimated the correlations Pinj between each pair of daily log-stock price shocks. The risk free rate is r. a. Describe in detail how you would go about pricing this option. b. How would you compute the unhedged 1% VaR for on the seller's potential payouts on this option? What are the assumptions you made in answering parts (a) and (b). d. What are the limitations of the methodology and assumptions you described in parts (a), (b), and (c) of this problem? c. i,T 3. You have been tasked with modeling and finding the price of a call option on a "market basket" of three assets. The option pays out max(0,(Y, K)) where Y, = 9,S1,1 +9292,7+q;$3,1, 9; is a portfolio weight, and S; is the stock price for stock i= 1, 2, and 3 at the end of day T. On day t= 0 (today) you observe the current stock prices (S.,0,S2,09930) and have estimated the mean drift rates Mi; and volatilities o, for each stock i. You have also estimated the correlations Pinj between each pair of daily log-stock price shocks. The risk free rate is r. a. Describe in detail how you would go about pricing this option. b. How would you compute the unhedged 1% VaR for on the seller's potential payouts on this option? What are the assumptions you made in answering parts (a) and (b). d. What are the limitations of the methodology and assumptions you described in parts (a), (b), and (c) of this problem? c