Suppose at time t = 0, you are given four default-free zero-coupon bond prices P(t, T) with

Question:

Suppose at time t = 0, you are given four default-free zero-coupon bond prices P(t, T) with maturities from 1 to 4 years:
P(0, 1) = .94, P(0, 2) = .92, P(0, 3) = .87, P(0, 4) .80
(a) How can you “fit” a spot-rate tree to these bond prices? Discuss.
(b) Obtain a tree consistent with the term structure given above,
(c) What are the differences, if any, between the tree approaches in Questions (a) and (b)?