Question 5 Consider a European put option on a non-dividend paying stock where the stock price is $22, the strike price is $19, the risk-free rate is 2% per annum, the volatility is 25% per annum and the time to maturity is 18 months. (a) Calculate u and d for a one-step binomial tree. (b) Compute the price of the put option for a one-step binomial tree using the replicating argument. (c) Instead of a one-step binomial tree, consider a three-step tree and the case of the European put option. Compute again u, d, qu and the put price using now the three-step binomial tree. (d) Calculate the delta of the stock option at each time step in (c) and explain what "rebalancing" the Delta means. (e) If the option in (c) is American instead of European, compute the price. In which nodes do you early exercise the option? (f) Using the put-call parity, to compute the price of the European call option with same strike, underlying and maturity of the European put in (c). If such call option is American instead of European, which is the price? Justify your answer. Question 5 Consider a European put option on a non-dividend paying stock where the stock price is $22, the strike price is $19, the risk-free rate is 2% per annum, the volatility is 25% per annum and the time to maturity is 18 months. (a) Calculate u and d for a one-step binomial tree. (b) Compute the price of the put option for a one-step binomial tree using the replicating argument. (c) Instead of a one-step binomial tree, consider a three-step tree and the case of the European put option. Compute again u, d, qu and the put price using now the three-step binomial tree. (d) Calculate the delta of the stock option at each time step in (c) and explain what "rebalancing" the Delta means. (e) If the option in (c) is American instead of European, compute the price. In which nodes do you early exercise the option? (f) Using the put-call parity, to compute the price of the European call option with same strike, underlying and maturity of the European put in (c). If such call option is American instead of European, which is the price? Justify your