Hull (9 ed.) states on p 707,
"Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate..."
He then states the usual short rate models such as Vasicek's, given by $$ dr = a(b - r)dt + \sigma dW. $$ The "economic" variables to be calibrated are
- $a$ = mean reversion speed
- $b$ = long term mean
- $\sigma$ = volatility.
What exactly is "economic" about these parameters? These seem like purely mechanical parameters, something to be tuned to the happenings of a time series. In fact, here's a time series of the 1-week LIBOR with daily observations - how is a diffusion model supposed to capture these stair step patterns, and then the puttering around zero for the last 6 years?
It seems dubious to attempt to calibrate a diffusion model in the hopes of capturing this observed behavior. Rather, I suppose a short rate modeler may decide on "regimes" in the data, and calibrate to only the data he feels best fits the current regime. But again - what "economic" assumptions am I making? Would a prudent modeler not calibrate to the data, and let that speak for itself? Is some senior manager with a PhD in economics supposed to have some insight into the values of the parameters and we use those instead?