Suppose you are given the following information on the spot rate rt:
• The rt follows:
drt = μrtdt + σrtdWt
• The annual drift is
μ = 0.01
• The annual volatility is
σ = 12%
• 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 five steps.
(b) What would be the implied u 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?