2. (55 points) You need to price an American put option on a non-dividend paying stock currently worth $50. The strike price is also $50. The risk-free rate is 10%, the time to expiration is six months, and the volatility is 40%. a) Calculate u, d, and p for a two-step binomial lattice with dt = 0.25, using the Jarrow-Rudd scheme for u and d. b) Value the option using a two-step binomial lattice. c) Is it optimal to exercise this option early at any time on the lattice? If so, where