The option delta (hedge ratio): A = Cu - Cd So(u-d) - 12.5-0. 50(1.25-0.8) = 0.56...

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The option delta (hedge ratio): A = Cu - Cd So(u-d) - 12.5-0. 50(1.25-0.8) = 0.56 It follows that an investor takes a long position in the stock to replicate the payoff of the call option. Moreover, her position in the synthetic option is 28 = 4.81 highly leveraged: Axs 5.82 The dollar position in T-bills Z= Cau-Cyd (u-d)(1+r) =C-Ax So = 5.82-28 = -$22.18 Question: Assume that the probability for the stock to go up is 60%. What are expected returns of the stock and the call option? P: 0.60 1-P: 0.4 U: 1.25 d: 0.8 = ER (Stock) P (Su) + 1-p. (Sd) ERStock = 0.60 (62.5)+0.4 (40) = 53.50 ER(call) = P.(Cu) + 1-p(c 0.60 (12.50) + 0.40(0) = 7.5 So: 50 Cu: 12.5 Cd:0 Question: What are the standard deviations of returns of the stock and the call option? Practice Problem. In the example above, what would be your arbitrage strategy if the call option were selling for $3? The option delta (hedge ratio): A = Cu - Cd So(u-d) - 12.5-0. 50(1.25-0.8) = 0.56 It follows that an investor takes a long position in the stock to replicate the payoff of the call option. Moreover, her position in the synthetic option is 28 = 4.81 highly leveraged: Axs 5.82 The dollar position in T-bills Z= Cau-Cyd (u-d)(1+r) =C-Ax So = 5.82-28 = -$22.18 Question: Assume that the probability for the stock to go up is 60%. What are expected returns of the stock and the call option? P: 0.60 1-P: 0.4 U: 1.25 d: 0.8 = ER (Stock) P (Su) + 1-p. (Sd) ERStock = 0.60 (62.5)+0.4 (40) = 53.50 ER(call) = P.(Cu) + 1-p(c 0.60 (12.50) + 0.40(0) = 7.5 So: 50 Cu: 12.5 Cd:0 Question: What are the standard deviations of returns of the stock and the call option? Practice Problem. In the example above, what would be your arbitrage strategy if the call option were selling for $3?