Applying Regulatory Shocks to Stressed Yield Curves
Summary
The document asks whether Basel-style steepening and flattening shocks to a US Treasury curve need further adjustments before use in valuation or regression models. In particular, it raises the possibility that stressed curves could imply arbitrage opportunities. The answer states that a risk-free zero curve, and its implied forward rates, do not create arbitrage in the way the question suggests, because the rates are defined as risk-free rates.
For regulatory stress testing, the answer advises following the prescribed shock methodology as written, since extra modifications may make the scenario noncompliant. It notes that specific regulations can prescribe shocks to maturity buckets, which may result in discontinuities or other structural features. The response is general rather than tailored to the cited Basel proposal, and it does not detail curve construction, interpolation, valuation-model inputs, or validation procedures. Users therefore need to consult the applicable regulation and model requirements to determine how the prescribed curve should be represented and used.
Key ideas
- A risk-free zero curve and its implied forward rates are not treated as sources of arbitrage in the answer.
- Regulatory stress scenarios should follow the prescribed methodology to preserve compliance.
- Some rules apply shocks to maturity buckets, which can produce a curve with structural irregularities.
- The response is general and does not provide specific curve construction or model validation guidance.
Tags
Full text
# Required adjustments for stressed yield curves # Required adjustments for stressed yield curves I was looking at Basel proposed interest rate shocks. Using the standard US Treasury Yield Curve for the period starting from September 2017 to August 2019, I was able to construct Steep and Flat scenarios as highlighted in the link above. In general, they do make sense given the current yield curve for US Treasuries: My question now is what further adjustments do these stressed curves need? One subject that comes to mind is the "no arbitrage-ness" of the curve. Do I have to make sure that the curve does not present arbitrage opportunity? If so, how? Any other adjustments that I need to make sure before feeding the stressed yields to valuation models and regression models with other risk factors? ## Answer by raptor22 (score 2, accepted) https://quant.stackexchange.com/a/48917 > My question now is what further adjustments do these stressed curves need? One subject that comes to mind is the "no arbitrage-ness" of the curve. Do I have to make sure that the curve does not present arbitrage opportunity? If so, how? No there is no such thing as arbitrage arising from a risk free zero curve. Any zero rate you get is by definition the risk free rate. Same for the implied forward rates. > Any other adjustments that I need to make sure before feeding the stressed yields to valuation models and regression models with other risk factors? I am not familiar with your specific regulation. From what I know of similar market risk regulations for insurances: you should just have to apply what is precisely described in that link. Applying any change to that would not be deemed compliant with the prescribed scenario. Note that this may not make sense... as these regulatory choices are often political and not based on facts. In some specific regulation you have to only apply a shock to one “bucket” of maturities at a time; so you are still lucky to have continuous zero curve :)
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.