# Question 1. Consider a two-step binomial tree, where a stock that pays no dividends has current price 100, and at each time step can increase by 20% or decrease by 10%. The possible values at times T = 2 are thus 144, 108 and 81. The annually compounded interest rate is 10%. a) Calculate the price of a two-year 106-strike European put using risk-neutral probabilities. b) Calculate the price of a two-year 106-strike European put using replication. c) Calculate the price of a two-year 106-strike American put using replication, and hence verify that the American put has price strictly greater than the European. d) Calculate the prices of a two-year 86-strike European put and American put. What is different from part (c)?

Question

Question 1. Consider a two-step binomial tree, where a stock that pays no dividends has current price 100, and at each time step can increase by 20% or decrease by 10%. The possible values at times T = 2 are thus 144, 108 and 81. The annually compounded interest rate is 10%.

a) Calculate the price of a two-year 106-strike European put using risk-neutral probabilities.

b) Calculate the price of a two-year 106-strike European put using replication.

c) Calculate the price of a two-year 106-strike American put using replication, and hence verify that the American put has price strictly greater than the European.

d) Calculate the prices of a two-year 86-strike European put and American put. What is different from part (c)?