Problem:
Suppose that x is the yield on a perpetual government bond that pays interest at the rate of 1$ per annum. Assume that x is expressed with continuous compounding, that interest is paid continuously on the bond, and that x follows the process:
dx = a(x(0) - x) dt + sx dz
Where a, x(0), and s are positive constants, and dz is a wiener process:
1) What is the process followed by the bond price?
2) What is the expected instantaneous return(including interest and capital gains) to the holder of the bond?