Construct an example showing (how the hedge works and illustrating how the hedge portfolio earns the risk-free rate in each period.

u2S = 156.25 US = 125 CU2 = 56.25 Cu = 31.54 V 2 = 701 (156.25) - 701(56.25) Vu = 701(125) - 1,000(31.54) - 9,430(1.07) = 56,085 = 60,010 Th = (56,085/52,410) - 1 = .07 Th = (60,010/56,080) - 1 = .07 hu = 1.0000 Buy 299 calls @ 31.54 ($9,430) udS = 100 S = 100 Borrow $9,430 Hold 701 shares @ 125, short 701 Cud = 0.00 C = 17.69 calls @ 31.54, debt of Vud = 701 (100) - 701 (0.0) h = 0.701 $9,430 -9,430(1.07) Hold 701 shares @ 100, short 1,000 = 60,010 calls @ 17.69 dS = 80 rh = (60,010/56,085) - 1 = .07 V = 701 (100) - 1,000(17.69) Cd = 0.00 Vdu = 0(100) - 1,000(0.00) = 52,410 Vd = 701 (80) - 1,000(0.00) + 56,080(1.07) = 56,080 = 60,006 Th = (56,080/52,410) - 1 = .07 Th = (60,006/56,080) - 1 = .07 hd = 0.00 Sell 701 shares @ 80 ($56,080) Invest $56,080 in bonds d2s = 64 Hold 0 shares @ 80, short 1,000 calls @ 0.00, hold Cd2 = 0.00 $56,080 in bonds Va2 = 0(64) - 1,000(0.00) + 56,080(1.07) = 60,006 Th = (60,006/56,080) - 1 = .07