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?
The solution provides the process followed by bond price.