Calibrating a Two-Factor Vasicek Model for Relative-Value Analysis
Summary
The document explains a two-stage use of a two-factor Vasicek term-structure model for assessing relative value along a swap curve. First, estimate the model’s fixed parameters, including mean-reversion and volatility-related quantities, from historical interest-rate data. Maximum likelihood estimation or Kalman filtering are mentioned as possible approaches, and this estimation stage can require substantial work.
Next, use the estimated model with the current yield curve. Rather than re-estimating the parameters, solve for factor values that make the model match selected maturities assumed to be fairly priced. In the example discussed, two points anchor the fitted curve; the model-implied rate at another maturity can then be compared with its observed market rate to judge whether it appears rich or cheap. This is a relative-value interpretation, not a guarantee that the selected anchor points are fair or that deviations will converge. The document offers a conceptual workflow, not code or a worked calibration, and the original question’s maturity references differ from the answer’s example.
Key ideas
- Estimate the Vasicek model’s parameters from historical interest-rate data before fitting a current curve.
- Maximum likelihood estimation and Kalman filtering are cited as parameter-estimation approaches.
- Current curve fitting solves for factor values while keeping the previously estimated model parameters fixed.
- Selected maturities serve as anchors assumed to trade fairly.
- Compare other market rates with model-implied rates to assess relative richness or cheapness.
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Full text
# Vasicek yield curve # Vasicek yield curve > Term structure is determined by a two-factor affine model (Vasicek). Using the monthly swap market data, we fit the model to match exactly the one-year and ten-year points along the swap curve each month. Once fitted to these points, we then identify how far off the fitted curve the other swap rates are. Above a quote what I'm working with and trying to get my head around what are my steps and would appreciate any help. Currently I'm able to do MLE estimation of short (1Y) and long (10Y) points, but I don't understand, how do I calibrate this to fit the initial curve. Without calibration, it is giving me very weird values for other maturities. Main tool I use is R, but really any code or good step-by-step example would help. ## Answer by Helin (score 3) https://quant.stackexchange.com/a/26128 This is a relative value application of equilibrium term structure models. There are really two steps in this exercise: Step 1 is a calibration procedure that gets you the model "parameters" (i.e., the mean reversion parameters, volatilities/correlation parameters, etc.). This is usually done using historical interest rate dat and either MLE or Kalman filtering techniques (see "Kalman Filtering of Generalized Vasicek Term Structure Models"). Once step 1 is done (which BTW is a huge undertaking), you can then apply the model for relative value analysis. Given today's yield curve (as opposed to historical data in step 1), you back out the "factor values" (as opposed to model parameters) so that your model fits a few points on the yield curve. In the example you used, the trader/researcher assume that 2- and 10-year yields are trading fair, and fit the model to match these two points. They then compare the model-implied value for, say, the 5-year point to judge whether or not the 5-year yield is trading rich/cheap.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.