Stress Testing Yield Curves Beyond a Calm Historical Sample
Summary
The question concerns risk models calibrated to a recent sample in which short-term GBP rates moved little. PCA and ARMA methods can generate plausible curves, yet calibration to that quiet period may produce scenarios that understate possible one-year rate shocks. The discussion identifies a general limitation: historical data may not capture future dynamics, even when the model can technically generate larger moves.
The answer recommends applying judgment by directly shifting the yield curve to a severe scenario and revaluing the portfolio, or by increasing rate volatility to probe larger outcomes. It argues that risk analysis should examine plausible stress cases instead of relying only on a model calibrated to a limited sample. The response offers no quantitative method for choosing shock sizes or volatility adjustments, and its suggested volatility multiplier is an illustrative, extreme intervention rather than a calibrated prescription. It also does not resolve how to estimate the probability of such scenarios.
Key ideas
- A quiet calibration period can lead a yield curve model to understate plausible rate moves.
- Directly shock the curve and revalue the portfolio to assess severe scenarios.
- Increasing modeled volatility can expose the portfolio to larger hypothetical movements.
- Risk judgment should supplement historical calibration when available data do not represent future dynamics.
- The answer does not provide a principled calibration method for selecting stress magnitudes.
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Full text
# How do you model yield curves for interest rates that have hardly moved? # How do you model yield curves for interest rates that have hardly moved? I have a model which I use to simulate future yield curves. The model uses some standard concepts, like PCA and ARMA models, and it creates some nice-looking yield curves. The simulated curves are used for risk purposes (VaR, stress testing, etc). The problem that I'm having is that I am working with 5 years of data of GBP swap rates / GBP yield curve, and during this period the short end of the curve hardly moves. For the short end of the curve we use something like LIBOR. Here's what 3M LIBOR has been doing since 2000: My dataset starts right after the big drop in 2009. As you can see, after 2009 the largest move over a year is maybe 50-70 bps, which is small. As a result my model simply doesn't produce large movements on the short end of the yield curve. I'm not producing movements larger than, say, 20-30 bps. This is problematic, since for the purposes of risk I want to be 99% "sure" that I've captured the worst-case scenario. And further back in history rates were much more volatile. It's unlikely, but not out of the question, that LIBOR increases by 100bps or more. (this is all over a time horizon of one year by the way) To counter this "flatness" I could maybe include GARCH effects and other fat-tailed distributions, but I'm guessing this hardly matters since calibrating to the data just results in, again, a very inert model. Also, the current model works reasonable for the EUR swap curve, which has been a more volatile. The model I'm using can definitely produce large rate movements -- it's just that the calibration to the the 5 year dataset results in relatively static model. So what else can I do? How can I "instruct" my model to simulate larger movements? Should I just start tuning the model parameters by hand? Should I look at the option market? Maybe add random interest rate shocks? I should note that one obvious "solution" to this problem is to include a larger dataset, but let's just assume that I can't increase my dataset (there's a few reasons for this). It's a general problem I suppose: what do you do when your historical dataset does not properly reflect potential future dynamics? ## Answer by dm63 (score 1) https://quant.stackexchange.com/a/25013 Well you have to be more flexible in your thinking. If you believe that a spike in libor might occur, you have to manipulate the model to produce that scenario. How about just moving the yield curve to that scenario and revaluing the portfolio. Or jack the libor volatilty by a factor of 20. This reminds me of why some banks blew up in the crisis. Faced with the situation you describe, they slavishly stick to some model approved by management, which doesn't probe the distribution enough, instead of using common sense!
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