The current 6-month and 1-year Treasury bills are trading at Pbill(0,0.5) = 97.531 and Pbill(0,1) = 95.1241, respectively. Consider now a binomial tree with root r1, u, and r1, d and r1, d as two interest rate scenarios after an upward or downward movement in the interest rate, respectively.
(a) What is r0
(b) Let p* = 0.5 be the risk neutral probability. Do you have enough information to pin down a unique value of r1, u and r1, d? Provide at least three examples of values of the pair (r1, u, r1, d) that are consistent with the two bond prices above. What is the difference across the three pairs of values?
(c) An option with payoff
Option payoff at 1 = 100 ( max(r1 - 5%, 0)
Is also trading at C0(l) = $0.97531. Do you now have sufficient information to pin down the pair (r1, u, r1, d)? Explain.
(d) Suppose you did not know p* = 0.5. What other information would you need to compute also p*? Provide an example.