Question: Consider a Black-Scholes model with r = 6%, sigma = 0.25, S(0) = 50 and delta = 0. Suppose you sold ten (10) 90-day Puts

Consider a Black-Scholes model with r = 6%, sigma = 0.25, S(0) = 50 and delta = 0. Suppose you sold ten (10) 90-day Puts with strike K = 50 (at price C_1 (0) determined by the Black-Scholes formula). You wish to hedge your risks and in particular are worried about the stock moving up and down. Using the underlying stock as well as 180-day Puts with strike K = 50 (priced at C_2 (0) again using the B-S formula) construct, a Delta-Gamma neutral portfolio. Suppose that you also invest in bonds such that the initial value of your portfolio is exactly zero. Thus your overall portfolio is V(0) = xS(0) + y = 10C_1 (0) + zC_2 (0), where x, z have been chosen to make V Delta- and Gamma- neutral at time zero in part (a), and y is chosen so that V(0) = 0. Produce a table listing the value of your portfolio tomorrow V(1/365) in the cases that the stock goes to S(1/365) = 48,50,52. Consider a Black-Scholes model with r = 6%, sigma = 0.25, S(0) = 50 and delta = 0. Suppose you sold ten (10) 90-day Puts with strike K = 50 (at price C_1 (0) determined by the Black-Scholes formula). You wish to hedge your risks and in particular are worried about the stock moving up and down. Using the underlying stock as well as 180-day Puts with strike K = 50 (priced at C_2 (0) again using the B-S formula) construct, a Delta-Gamma neutral portfolio. Suppose that you also invest in bonds such that the initial value of your portfolio is exactly zero. Thus your overall portfolio is V(0) = xS(0) + y = 10C_1 (0) + zC_2 (0), where x, z have been chosen to make V Delta- and Gamma- neutral at time zero in part (a), and y is chosen so that V(0) = 0. Produce a table listing the value of your portfolio tomorrow V(1/365) in the cases that the stock goes to S(1/365) = 48,50,52

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