Question 2

Question 2 - number really big Finding VaR(0.9,n X-16.14 A3...

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S0 K1 K2 mean sd T 1000 1200 800 0.12 0.35 0.1 Let A1 = (ln(800/1000)-(0.12-0.35^2/2)*0.1)/(0.35*sqrt(0.1)) = -2.07 A2 = (ln(1200/1000)-(0.12-0.35^2/2)*0.1)/(0.35*sqrt(0.1)) = 1.59 Probability A1 and A2 with N(0,1) Gamma(A1)= 0.02 Gamma(A2)= 0.94 Let A3 = (ln((VaR(alpha,n)+1200)/1000)-(0.12-0.35^2/2)*0.1)/(0.35*sqrt(0.1)) A4 = (ln((800-VaR(alpha,n))/1000)-(0.12-0.35^2/2)*0.1)/(0.35*sqrt(0.1)) Note (0.12-0.35^2/2)*0.1 = 0.01 0.35*sqrt(0.1) =  0.11 Let X = VaR(alpha,n) F(VaR(alpha,n)) = 1+Gamma(A1)-Gamma(A2)+Gamma(A3)-Gamma(A4) = alpha 1. Using "Goal Seek" to calculate interest rates. 2. I mutiply by 1000*F(VaR(alpha,n))= 1000*alpha because "Goal Seek" does not treat decimal really well, so I make the
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Unformatted text preview: number really big Finding VaR(0.9,n) X-16.14 A3 = 1.47 A4 =-1.89 Gammma(A2)-Gamm(A1)+Gamma(A1)-Gamma(A2) 0.07 Gamma(A3) 0.93 Gamma(A4) 0.03 1000*F(VaR(alpha,n)) = 900 Finding VaR(0.95,n) X 21.45 A3 = 1.75 A4 =-2.31 Gammma(A2)-Gamm(A1)+Gamma(A1)-Gamma(A2) 0.07 Gamma(A3) 0.96 Gamma(A4) 0.01 1000*F(VaR(alpha,n)) = 950 Finding VaR(0.99,n) X 103.74 A3 = 2.34 A4 =-3.32 Gammma(A2)-Gamm(A1)+Gamma(A1)-Gamma(A2) 0.07 Gamma(A3) 0.99 Gamma(A4) 1000*F(VaR(alpha,n)) = 990 Finding VaR(0.99,n) X 216.11 A3 = 3.09 A4 =-4.91 Gammma(A2)-Gamm(A1)+Gamma(A1)-Gamma(A2) 0.07 Gamma(A3) 1 Gamma(A4) 1000*F(VaR(alpha,n)) = 999...
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