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 (. h stands for "high volatility" and ( stands for "low volatility." Node h at Date 1 is followed bv either hu or hd at Date 2 and node l at Date 1 is followed by either lu or ld at Date 2. This question is about comparing options prices at the high-volatilitv node h and at the low-volatility node (. 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 B,-Bd-1/2 and B0-1/4 The stock prices are as follows: Sh SI-20, Shu-80, Shd-0, Se,-60, and Se,-20