In this exercise, we numerically verify that the probabilities derived for European calls also work for other contracts by (i) valuing the contracts starting from the value of a call, and (ii) by checking whether a risk-adjusted probability evaluation provides the same answer.

Consider the example used in Section ??. The data used were u = 1.1, d = 0.9, (1 + r) = 1.05, (1 + r∗) = 1.0294118, S0 = 100; for our call, X = 95. The tree, including the (risk-adjusted) probabilities for time 2, is reproduced below; ignore the columns added to the right, initially

(a) Compute the call value using the binomial model.
(b) Compute the two-period forward rate directly (using Interest Rate Parity), and indirectly (using our risk-adjusted probabilities, that is, as CEQ0 (S2)).
(c) Compute the present value of an "old" forward purchase struck at Ft0,2 = 95 directly (using the formula in Chapter 3), and indirectly (using q).
(d) Value a European put with X = 95 directly (using Put Call Parity), and indirectly (using q).

EUR T-bill rob C P Forward at 95 at 95 at 95 21 0.36 26 0 26 110 100 99 0.48 0 4 90 81 0.16 0 14 -14