# What instruments can be used to calibrate short-rate models?

What type of debt instruments can be used to estimate short-rate model parameters?

How can I find the history of short-rate?

My guesses are overnight LIBOR/SOFR or extrapolation through the yield curve fitted on T-bills. According to my understanding yield curve may also be used. In the case of discrete-time, it should be the yield of the bond that matures the next day.

• What you mention will give you a good fitting of the rate term in your model, but note that you would also need swaptions or cap/floorlets for the volatility.
– KT8
Apr 13, 2022 at 11:50
• I didn't mention that I focus on local markets (in Hungary) so I tried to find analogous instruments. These are LIBOR and T-bills. These have different target audiences. So what should I use if I have access to both 3-month T-Bill data and 3-month BUBOR data (the Hungarian equivalent of LIBOR)? Apr 13, 2022 at 11:59
• Note that the T-Bill and BUROR data, as you mention, are different underlyings. You should fit one model for T-Bills and a another one for BUROR, trying to fit both at the same time would not work (actually, the same applies for BUROR 6M as compared to BUROR 3M, for example).
– KT8
Apr 13, 2022 at 17:24
• Thank you for your explanation. Apr 14, 2022 at 11:20

The purpose of the short rate model is to describe the evolution of an instantaneous short rate and hence make it possible to obtain discounting factors $$P(t,T)$$ as the expectation of the integral of the instantaneous short rate. Since the instantaneous short rate is not directly observable in the market, these models are calibrated to the option market using complex closed form formulas for vanilla caps/floors or swaptions. In the absence of a liquid options market you may be tempted to estimate model parameters from historical interest rate data, however this isn't the way they were supposed to work.