Hull–White One-Factor Calibration and Monte Carlo Pricing Errors

Summary

The document describes a calibration problem for a one-factor Hull–White interest rate model with constant mean reversion and volatility. The author reports that Monte Carlo prices match market prices for three swaptions in a set of four, while the first, with a one-year expiry and four-year tenor, is priced substantially higher. The model reproduces the initial term structure, but the calibration error raises questions about instrument selection and acceptable pricing tolerances.

The author also asks whether calibration for a standalone ten-year interest rate swap used in CVA analysis should emphasize swaptions near the period of peak exposure, and whether a trinomial tree's better fit points to a Monte Carlo implementation problem. Potential causes raised include Euler discretization and the forward-based theta function. The document offers no resolution or numerical error threshold, so it serves as a diagnostic question rather than a calibration method or demonstrated conclusion.

Key ideas

• A constant-parameter Hull–White one-factor model can fit some calibration swaptions while materially mispricing another.
• The model's ability to recover the initial term structure does not by itself resolve swaption pricing discrepancies.
• Calibration instrument choice may depend on the exposure profile relevant to a CVA application.
• A better trinomial-tree fit than Monte Carlo pricing can motivate checks of discretization and the theta implementation.
• The document does not establish a standard acceptable calibration error.

Tags

# Hull white model calibration - constant mean reverse factor and sigma


# Hull white model calibration - constant mean reverse factor and sigma












I setup a HW 1F model using Monte Carlo simulation with constant mean reversion and volatility factors. When I calibrate to a series of swaptions ( 1x4yr;2x3yr;3x2yr;4x1yr),the last three swaption prices match the market quite well, but the price of first (1x4yr) swaption from the MC Simulation is much higher than market price, the model also can recover initial term structure. Hope someone can help me on the following questions.

- how many swaptions are typically used in calibration of a HW1F model with constant factors.

- what is the acceptable pricing error (%) in HW1F calibration

- To calculate CVA for a stand-alone 10 yr IRS using HW1F, is it appropriate to focus on the around the max exposure area when I calibration the model, i.e. 3-5 year, rather than the whole scope?

- I also setup a HW1F trinomial tree (exact Theta), and it's calibrated to swaptions much better than the MC simulation, does that indicate my MC Simulation has issues (Euler discretization, theta function from forward)?

Thanks!

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.