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Question - One-Step and Two-Step Binomial Trees for Option Pricing
Shares in XYZ Corporation sell today for $20. The risk-free rate is 3% (continuously compounded). In the next six months, XYZ shares will either increase in price by 30%, or decrease in price by 40%. In the following six months, XYZ shares will again either increase in price by 30%, or decrease in price by 40%. XYZ pays no dividends.
(1) What is the price of a European call with strike price $19 and expiration in 6 months? Calculating the price explicitly using a binomial tree and the dynamic hedging/replicating method.
(2) What is the price of a European put with strike price $19 and expiration in 6 months? Calculating the price explicitly using a binomial tree and the dynamic hedging/replicating method, and verify that put-call parity holds, together with your solution for (1).
(3) If the put of part (2) currently trades for $1, is there an arbitrage? If, so describe one. If not, why not?
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