Suppose you are given the following information on the spot rate rt:
The rt follows:
dt =μrt + σrt dWr.
The annual drift is
μ= .01.
15This is the wise because the forward price, Ft], belt belong to the same forward date unlike, say, the Ct, which is a value expressed in time t dollar.
The annual volatility is
σ = 2%.
The current spot rate is assumed to be 6%.
(a) Suppose instruments are to be priced over a year. Determine an appropriate time interval ?, such that binomial trees have live steps.
(b) What would be the implied μ and d in this case?
(c) Determine the tree for the spot rate rt.
(d) What are the "up" and "down" probabilities implied by the tree?