(15 Points) Write a simulation which identifies the loss distribution for the portfolio using the full, linearized and second order (with the ad- justments in note (ii)) loss operators. As in class, produce a histogram approximation of the probability density functions. How well do the approximations work? For parameters use = 0.15475, = 0.2214, r = 0.0132, t = 0, T = .25, = 10/252 (ten day horizon), S0 = 158.12, K = 170 and M = 100 options. Run N = 100, 000 trials.

provide python code

b) (15 Points) Write a simulation which identifies the loss distribution for the portfolio using the full, linearized and second order (with the adjustments in note (ii)) loss operators. As in class, produce a histogram approximation of the probability density functions. How well do the approximations work? For parameters use =0.15475,=0.2214,r=0.0132,t=0,T=.25, =10/252 (ten day horizon), S0=158.12,K=170 and M=100 options. Run N=100,000 trials