Hedge Ratio = [P(+) - P(-)]/[S(+) - S(-)] = [MAX(120-160)-MAX(120-80)]/[160-80] = (0-40)/80 = -0.5
b1. 1 share & 2 stocks (will be delta neutral hedged portfolio).
At end of period,
if ST = S(+) = 160, Portfolio value VT = S(+) + 2*MAX(120- S(+),0) = 160 + MAX(120-160,0) = 160+0 = 160
if ST = S(-) = 80, Portfolio value VT = S(-) + 2*MAX(120- S(-),0) = 80 + 2*MAX(120-80,0) = 80+2*40 = 160
Hence (nonrandom) payoff to this portfolio = $160.
b2. PV(Portfolio) = 160/1.12 = 142.8571429 = $ 142.86.
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