Exercise 5.4 Suppose that r is the short-term interest rate (expressed in percentage on a yearly basis) and that it is modeled by a Feller process with parameters

α = 0.6, β = 2.25, σ = 0.5.

(a) Find the stationary distribution of the process.

(b) Define X(t) = 1 36000 r(t/360), t ≥ 0. Interpret X and find its distribution.

(c) Suppose that the market price of risk is q(t, r) = 0.25/

√

r − 0.02

√

r.

What is the distribution of ˜r under the equivalent martingale measure?

Also find the limiting behavior of the annual yield R(t, T ) on a zerocoupon bond, as T →∞.

(d) Suppose that under the equivalent martingale measure, ˜r is a Feller process with parameters a = 0.6 and b = 2.75. Find the associated market price of risk.