I AMERICAN PUT ON THE Two-STEP TREE Consider a two-step binomial tree. There are three dates, Date 0, Date 1, and Date 2, and two securities, a risky stock S and a risk-free bond B. At Date 2 there are four states, called hu, hd, lu, and ld. At Date 1 there are two nodes, called h and l. h stands for high volatility and l stands for low volatility. Node h at Date 1 is followed by either hu or hd at Date 2 and node l at Date 1 is followed by either l u or ld at Date 2. This question is about comparing options prices at the high-volatility node h and at the low-volatility node l. Note that at each of these nodes you have just a usual binomial model. The net interest rate on the bond is r = 1, so Bu = Ba = 1/2 and Bo = 1/4. The stock prices are as follows: Sh = Se = 20, Shu = 80, Shd = 0, Seu = 60, and Sea = 20. 1. Here we compute the stock returns at Date l at each node, h and l. a) Compute the gross returns on the stock at node h. Call these returns un when the stock price increases between Date 1 and Date 2 and d, when the stock price decreases between Date 1 and Date 2