A stock price evolves in a standard binomial tree. Each period it can either go up to u=1.1 times its previous price or down to d=0.9 times its previous price. Consider a two-period model (t=0, 1 , and 2), as depicted below. The risk-free (net) return between t=0 and t=1 is r1=5%, while between t=1 and t=2 it is r2=6%. The initial stock price is S=120 and the stock pays no dividends. t=0t=1t=2 (a) Price a European call option on the stock with strike price K=110 and maturity at t=2 using risk-neutral pricing. [6 marks] (b) How would you replicate the European call option at the u node at time 1,cu. Compute d and 0 as well. Comment on the three values of . [8 marks] (c) Explain in words why the price of the American call option with K=110 and maturity at t=2 is the same as the price of the European call option in part (a). [6 marks] (d) Price a European put option and an American put option on the stock with strike price K=119 and maturity at t=2 using risk-neutral pricing. [10 marks] (e) An average price Asian put option with maturity at t=2 gives the payoff max(KSavg,0) to the buyer, where Savg=3S0+S1+S2, and no early exercise is possible. Assume that K=120. Price this option using risk-neutral pricing. [10 marks ] A stock price evolves in a standard binomial tree. Each period it can either go up to u=1.1 times its previous price or down to d=0.9 times its previous price. Consider a two-period model (t=0, 1 , and 2), as depicted below. The risk-free (net) return between t=0 and t=1 is r1=5%, while between t=1 and t=2 it is r2=6%. The initial stock price is S=120 and the stock pays no dividends. t=0t=1t=2 (a) Price a European call option on the stock with strike price K=110 and maturity at t=2 using risk-neutral pricing. [6 marks] (b) How would you replicate the European call option at the u node at time 1,cu. Compute d and 0 as well. Comment on the three values of . [8 marks] (c) Explain in words why the price of the American call option with K=110 and maturity at t=2 is the same as the price of the European call option in part (a). [6 marks] (d) Price a European put option and an American put option on the stock with strike price K=119 and maturity at t=2 using risk-neutral pricing. [10 marks] (e) An average price Asian put option with maturity at t=2 gives the payoff max(KSavg,0) to the buyer, where Savg=3S0+S1+S2, and no early exercise is possible. Assume that K=120. Price this option using risk-neutral pricing. [10 marks ]