I have a question concerning the "choice" of parameters for the Vasicek model (formula below).
Consider me as a moron with below average level in maths haha. What I've done is basically run the Vasicek on Excel and compare it with the term structure of bonds. Then I used the solver to give me the parameters r, sigma, theta and kappa to minimize the squared error between my Vasicek and the market data.
Obviously it's a kitchen sink result, I have a very good fit but the underlying economic meaning is lost. So I thought about constraining sigma and theta in my solver, but how should I choose my constraint levels?
I was thinking about checking the average or moving average of the short term rate and its volatility over a few years and set them as a boundary.
I'm not looking for something perfect or complicated at all, I just want my parameters to make a little more sense, am I in the right direction?