You have a portfolio of derivatives 11 that is A-neutral but has the following Gamma, Gamma(Product) = -30. In the market there is a derivative U_1 with Gamma(U_1) = 0.4 and Delta (U_1) = 0.5. Explain how you should modify your portfolio (using U_1 and the underlying asset) to make it both Delta-and Gamma-hedged. Give the precise numerical quantities involved. If the price of U_1 is 1.50 and the price of the underlying is $2, what is the total cost of this modification? Formulas that may be potentially useful: F = S_0 e^(r-delta)^T F = S_0 e^rT - FV_T (Di upsilon) C - P = PV(F - K) R = sigma_i P(0, T_i)F(T)i)/sigma_i P(0, T_i) S_nh = S_0 d^n (u/d)^x, X ~ Bin(n, q) u = e^(r-delta)h+sigma Squareroot h d = e^(r-delta)h-sigma Squareroot h q = e(r-delta)h-d/u-d C = e^-rh (qC_u + (l-q)Cd) Delta = e^delta h C_u - C_d/S_u - S_d B = e^rh (uC_d - dC_u)/(u - d) C = Delta S + B C_0 = e^-delta T S_0 N (d_1) - Ke^-rT N(d_2) P_0 = Ke^-rT N (-d_2) -e^-delta T N S_0 N (-d_1) d_1, 2 = log(S_0/K) + (r - delta) T plusminus sigma^2 T/2/sigma Squareroot T Delta_Call = e^-delta M (d_1) Delta_Put = -e^-delta T N(-d_1) S_t = S_0 e(r-delta-sigma^2/2)t + sigma Squareroot t epsilon epsilon ~ N (0 1) E[S_t] = S_0e?^(r-delta)t You have a portfolio of derivatives 11 that is A-neutral but has the following Gamma, Gamma(Product) = -30. In the market there is a derivative U_1 with Gamma(U_1) = 0.4 and Delta (U_1) = 0.5. Explain how you should modify your portfolio (using U_1 and the underlying asset) to make it both Delta-and Gamma-hedged. Give the precise numerical quantities involved. If the price of U_1 is 1.50 and the price of the underlying is $2, what is the total cost of this modification? Formulas that may be potentially useful: F = S_0 e^(r-delta)^T F = S_0 e^rT - FV_T (Di upsilon) C - P = PV(F - K) R = sigma_i P(0, T_i)F(T)i)/sigma_i P(0, T_i) S_nh = S_0 d^n (u/d)^x, X ~ Bin(n, q) u = e^(r-delta)h+sigma Squareroot h d = e^(r-delta)h-sigma Squareroot h q = e(r-delta)h-d/u-d C = e^-rh (qC_u + (l-q)Cd) Delta = e^delta h C_u - C_d/S_u - S_d B = e^rh (uC_d - dC_u)/(u - d) C = Delta S + B C_0 = e^-delta T S_0 N (d_1) - Ke^-rT N(d_2) P_0 = Ke^-rT N (-d_2) -e^-delta T N S_0 N (-d_1) d_1, 2 = log(S_0/K) + (r - delta) T plusminus sigma^2 T/2/sigma Squareroot T Delta_Call = e^-delta M (d_1) Delta_Put = -e^-delta T N(-d_1) S_t = S_0 e(r-delta-sigma^2/2)t + sigma Squareroot t epsilon epsilon ~ N (0 1) E[S_t] = S_0e?^(r-delta)t