5. The price of Apple is $197 today. Its annualized volatility in the past year is 20%. Consider a call option expiring in 6 months with strike price K=195. Assume the interest rate is 0. (1) In a one-period binomial tree model, calculate the risk neutral probability q, parameters u and d. Recall that u = e and d = eT, where is the annualized volatility and T is period in years. (2) Calculate the price of the call option in this one-period model (3) Calculate the price of the call option in a two-period model (note that in this case, T is 3 months instead of 6 months, so you have to re-calculate q, u and d) (4) Extra credit: using computer programs or by hand, compute the option price under a 5- period binomial tree model (5pts, and the total score on this problem set cannot exceed 100) 1. (Arbitrage-free condition) Consider a one-period binomial model with risk-free interest rate r0, up factor u > 0, and down factor d > 0. Prove that the one-period binomial model is arbitrage-free if and only if d