The Vasicek interest rate stochastic differential equation (4.4.32) is
where a, ß, and s are positive constants. The solution to this equation is given in Example 4.4.10. This exercise shows how to derive this solution.
(i) Use (4.4.32) and the It-Doeblin formula to compute d(eßt R(t) ) . Simplify it so that you have a formula for d(eßt R(t)) that does not involve R(t) .
(ii) Integrate the equation you obtained in (i) and solve for R(t) to obtain (4.4.33) .