= (b) (8 points) Consider a portfolio consisting of one European call option and one put option on a non-dividend paying stock. Suppose that the value of the stocks S1 and S2 at time tn is Sn,1 110 and Sn,2 90 respectively. For both stocks the volatility is o = 0.2, the maturity time is T =1+tn, r = 0.02 and the exercise price is K = 100. Assume that the risk factor changes for the time horizon At 250 is the log returns X (In(Sn+1,1) In(Sn,1), In(Sn+1,2) - 0.2 0.4 -0.1 In(Sn,2)) of the the two stocks which follow N2 ( 0.1 -0.1 0.4 Use the Variance-Covariance Method to estimate the VaR and ES for the portfolio loss from today until tomorrow at level a = 95%. The Greeks of the call options take the values CBS(tr, Sn,1) ~ -4.8299, CBS(tr, Sn,2) ~ -3.9903 :)) and CBS(tn, Sn,1) 0.7507, CBS(tn, Sn,2) 0.3719. = (b) (8 points) Consider a portfolio consisting of one European call option and one put option on a non-dividend paying stock. Suppose that the value of the stocks S1 and S2 at time tn is Sn,1 110 and Sn,2 90 respectively. For both stocks the volatility is o = 0.2, the maturity time is T =1+tn, r = 0.02 and the exercise price is K = 100. Assume that the risk factor changes for the time horizon At 250 is the log returns X (In(Sn+1,1) In(Sn,1), In(Sn+1,2) - 0.2 0.4 -0.1 In(Sn,2)) of the the two stocks which follow N2 ( 0.1 -0.1 0.4 Use the Variance-Covariance Method to estimate the VaR and ES for the portfolio loss from today until tomorrow at level a = 95%. The Greeks of the call options take the values CBS(tr, Sn,1) ~ -4.8299, CBS(tr, Sn,2) ~ -3.9903 :)) and CBS(tn, Sn,1) 0.7507, CBS(tn, Sn,2) 0.3719