= 3) Consider the positive strict local martingale (St)te[0,1] solution of dst SdBt with S, > 0, where St has the probability density function So (1/2 - ) (1/x + 1/S02 ( exp exp x > 0, t (0,T]. 231270 2t a) (5 marks) Plot a sample graph of (St)te[0,1] with T = 1, and attach or upload it with your submission. Als) SERT ((-1/2=1/5") - (-144,1? 80%)) 2t b) (10 marks) Compute E(ST) and check that the condition of Question (1c) is satisfied. Hint: Use the change of variable y = 1/.0 and the standard normal CDF O. c) (10 marks) Compute the limit of E[ST] as So tends to infinity. d) (10 marks) Compute the price E[(St K)+] of a European call option with strike price K > 0 in this model, assuming a risk-free interest rate r = 0. Hint: The final answer should be written in terms of the standard normal CDF and of the normal PDF 4. e) (5 marks) Show that E[(ST-K)+) is bounded uniformly in So > 0 and K >0 by a constant depending on T >0. = 3) Consider the positive strict local martingale (St)te[0,1] solution of dst SdBt with S, > 0, where St has the probability density function So (1/2 - ) (1/x + 1/S02 ( exp exp x > 0, t (0,T]. 231270 2t a) (5 marks) Plot a sample graph of (St)te[0,1] with T = 1, and attach or upload it with your submission. Als) SERT ((-1/2=1/5") - (-144,1? 80%)) 2t b) (10 marks) Compute E(ST) and check that the condition of Question (1c) is satisfied. Hint: Use the change of variable y = 1/.0 and the standard normal CDF O. c) (10 marks) Compute the limit of E[ST] as So tends to infinity. d) (10 marks) Compute the price E[(St K)+] of a European call option with strike price K > 0 in this model, assuming a risk-free interest rate r = 0. Hint: The final answer should be written in terms of the standard normal CDF and of the normal PDF 4. e) (5 marks) Show that E[(ST-K)+) is bounded uniformly in So > 0 and K >0 by a constant depending on T >0