You have a portfolio of derivatives Product that is Delta-neutral but has the following Gamma, Gamma(Product) = -30. Ill 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? F = S_0e^(r - delta)^T F = S_0e^tT - 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_0d^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) - d/u - d C = e^-rh (qC_u + (1 + q)C_d) Delta = e^-delta h C_u - C_d/S_u - S_d B = e^-rh (u C_d - d C_u)/(u - d) C = Delta S + B C_0 = e^-delta T S_0 N(d_1) - K e^-rT N(d_2) P_0 = K e^-rT N(-d_2- e^-delta T S_) 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 T N(d_1) Delta_Put = -e^-dela T N(-d_1) S_t = S_) e^(r-delta-sigma^2/2)t+sigma Squareroot t epsilon, epsilon ~ N (0, 1) E[S_t] = S_0 e^(r-delta)t