Calibrating Hull–White from Historical IBOR Curves Without Derivative Prices
Summary
This document raises practical and statistical questions about estimating a Hull–White short-rate model in a market where interest-rate derivatives are not publicly traded. The researcher has historical VNIBOR curves and is considering whether a three-month IBOR rate can stand in for the instantaneous short rate, given concerns about overnight-rate volatility. The discussion also asks whether using a forward rate consistent with the observed tenor would be more appropriate than treating that tenor as an instantaneous rate.
A proposed historical-variance approach compares rate changes after subtracting a forward curve observed at the start of each window with the model’s theoretical variance, then fits mean-reversion and volatility parameters across window lengths. The author questions whether this adjustment adequately isolates model-rate variation, and whether rates of different maturities can share the same parameters when their underlying exposures differ. The text presents these as unresolved modeling choices, not validated answers. It provides no derivative-price calibration, empirical results, or final parameter estimates, so the suggested method requires further theoretical and market-specific validation.
Key ideas
- The document considers using historical IBOR curves to estimate Hull–White parameters when derivative prices are unavailable.
- A three-month IBOR rate may not behave like an instantaneous short rate, so tenor assumptions need scrutiny.
- Subtracting the initial forward curve is proposed as a way to isolate rate variation across historical windows.
- The author questions whether different IBOR maturities represent sufficiently similar risks to share model parameters.
- The proposed variance-fitting approach is exploratory and is not supported by reported validation or estimates.
Tags
Full text
# How to calibrate short-rate model (Hull-White) using historical domestic IBOR curve without other derivative price?
# How to calibrate short-rate model (Hull-White) using historical domestic IBOR curve without other derivative price?
I'm trying to calibrate Hull White model in VietNam market to value IRS, CSS products which are not publicly traded.
```
dr(t)=(θ(t)−αr(t))dt+σ(t)dW(t)
```
I only have historical VNIBOR curves data, we do not have trading interest derivatives yet.So basically we have R_i(0,1/250), R_i(0,1/4), R_i(0,1/2), ... for observation date i. I have done some research and got some confusions:
- Some banks use IBOR 3M as a surrogate for instantaneous rate (fit with theoretical formula of r(t)). The reason was Overnight rate is too volatile. But is it too inaccurate to consider 3M as instantaneous? If cant use Overnight rate and has to use 3M rate, why don't we use a theoretical formula of R(t,t+3M)?
- Some papers suggest using historical variance of r_i (if we use IBOR 3M as surrogate for instantaneous rate, r_i will be R_i(0,3M) data) as estimation for Var(r(t)) = σ^2*(1-exp(-2at))/a.
However, the r(t) process in HW model doesn't have fixed mean like in Vasicek model.
So historical variance of r_i should contains both variance of r(t) and F(0,t) Should we use the historical variance of the new series x_i = r_(i+t) - F_i(0,t)?
- I've read that we shouldn't use different maturities (e.i VNIBOR 3M and VNIBOR 6M) in 1 calibration because they has different underlying. Refer @castella08's comment here What instruments can be used to calibrate short-rate models? Does it mean for each s, R_i(0,s) should have different risk neutral parameters (a,σ)? However, in HW model, when we calculate the mean parameter θ(t) and F(0,t) in the E(r(t)) formula, we have to use different maturities R_i(0,s) with the same (a,σ). Does it conflict with the idea above?
- My first approach is using the variance of x_i = r_(i+t) - F_i(0,t) as estimation of theoretical Var(r(t)) for different "window of view" t. F_i(0,t) observed at time i and r_(i+t) observed at time i+t. Then try to find (a,σ) that best fit those variances with theoretical formulas. Is it appropriate? If in practice Overnight rate is too unreliable, could I change to something like x_i = R_(i+t)(0,3M) - F_i(0,t,t+3M), I'm not sure the formula for 3M rate yet, as estimation of theoretical Var(R(t,t+3M)) formula?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.