12 10 10 8 6 4 2 Condor Payoff 0 50 70 90 ST 110 130...

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12 10 10 8 6 4 2 Condor Payoff 0 50 70 90 ST 110 130 150 Figure 1: Condor Payoff at T = 1 year Question 4: Binomial Trees for Option Pricing (4/10) Shares in XYZ Corporation sell today for $100. The risk-free rate is 10% (continuously compounded, annual). In the next 1 month, XYZ shares will either increase in price by 25%, or decrease in price by 20%, with the same probability. XYZ pays no dividends. One-Step Binomial Tree (i) What is the price of a European call with strike price $120 and expiration in 1 month? Calculate the price explicitly using a binomial tree and the hedging/replicating method. (ii) If the call of part (i) currently trades for $2, is there an arbitrage? If so, describe one. If not, why not? Risk-Neutral Pricing (iii) What is the price of a European put with strike price $120 and expiration in 1 month? Calculate the price explicitly using risk-neutral probabilities (the risk-neutral pricing method), and verify that put-call parity holds, together with your solution for (i). Multi-Step Binomial Tree (4) Suppose for each month, XYZ shares will either increase in price by 25%, or decrease in price by 20%, with the same probability. What is the price of a European put with strike price $120 and expiration in 3 months? You can calculate the price using multi-step binomial tree by hand or use the excel sheet "BinomialTree.xls" (put the screen shots of your excel Sheet 1 and Sheet 2 in your submission if you use the excel sheet). 12 10 10 8 6 4 2 Condor Payoff 0 50 70 90 ST 110 130 150 Figure 1: Condor Payoff at T = 1 year Question 4: Binomial Trees for Option Pricing (4/10) Shares in XYZ Corporation sell today for $100. The risk-free rate is 10% (continuously compounded, annual). In the next 1 month, XYZ shares will either increase in price by 25%, or decrease in price by 20%, with the same probability. XYZ pays no dividends. One-Step Binomial Tree (i) What is the price of a European call with strike price $120 and expiration in 1 month? Calculate the price explicitly using a binomial tree and the hedging/replicating method. (ii) If the call of part (i) currently trades for $2, is there an arbitrage? If so, describe one. If not, why not? Risk-Neutral Pricing (iii) What is the price of a European put with strike price $120 and expiration in 1 month? Calculate the price explicitly using risk-neutral probabilities (the risk-neutral pricing method), and verify that put-call parity holds, together with your solution for (i). Multi-Step Binomial Tree (4) Suppose for each month, XYZ shares will either increase in price by 25%, or decrease in price by 20%, with the same probability. What is the price of a European put with strike price $120 and expiration in 3 months? You can calculate the price using multi-step binomial tree by hand or use the excel sheet "BinomialTree.xls" (put the screen shots of your excel Sheet 1 and Sheet 2 in your submission if you use the excel sheet).