2. 2.1 Consider the binomial model with u = 1.25, d = 0.8, risk-free rate of 10% and initial asset price so = 100. Calculate the price of an American put option with exercise price K = 100 and n = 4 periods of one year each left until expiry. [15%] 2.2 Calculate the price of an option in the setting of 2.1 which, at the end of the third period, gives its holder the right to purchase the underlying asset at the minimum price realised over the life of the option. (The option maturity is three years with each binomial tree time step being 1 year. The asset price at the final node is also included in the calculations.) [20%] 2.3 A stock price is currently 30. During each 2-month period for the next 6 month it will increase by 8% or reduce by 10%. The annual risk-free interest rate is 5% (continuous com- pounding). Use a three-step binomial tree to calculate the value of a derivative (called turbo option) that pays off St * (30 - St), where St is the stock price in 6 months. [15%] 2. 2.1 Consider the binomial model with u = 1.25, d = 0.8, risk-free rate of 10% and initial asset price so = 100. Calculate the price of an American put option with exercise price K = 100 and n = 4 periods of one year each left until expiry. [15%] 2.2 Calculate the price of an option in the setting of 2.1 which, at the end of the third period, gives its holder the right to purchase the underlying asset at the minimum price realised over the life of the option. (The option maturity is three years with each binomial tree time step being 1 year. The asset price at the final node is also included in the calculations.) [20%] 2.3 A stock price is currently 30. During each 2-month period for the next 6 month it will increase by 8% or reduce by 10%. The annual risk-free interest rate is 5% (continuous com- pounding). Use a three-step binomial tree to calculate the value of a derivative (called turbo option) that pays off St * (30 - St), where St is the stock price in 6 months. [15%]