Consider a compound put option on a put option (put on a put) which gives the right to sell at time T> 0 a put option for a price K. The underlying put option is written on a stock with strike price K2 and maturity T2 > T. The simplest model for pricing a compound put option is a two-step binomial tree model with time steps T and T. Use a two-step binomial tree model to compute today's (t = 0) arbitrage-free price of a put on a put with T 1 and T = 2 (measured in years). The current stock price is So = $50 and over each of the next two one-year periods it is expected to go up by 20% or down by 20%. The strike price of the put option on the stock (with maturity T 2) is K = $52, and the strike price of the compound put option on the put option (with maturity T = 1) is K = $5. Assume that the risk-free interest rate is 5% per annum. =