Using Principal Components to Stress a Zero-Coupon Yield Curve
Summary
The document describes a proposed stress-testing exercise for a zero-coupon yield curve built from daily observations. The curve combines a money-market-based short tenor with longer tenors interpolated from secondary-market Treasury rates. The author divides maturities into short, medium, and long segments, observes that the shortest rate is unusually volatile, and reports that volatility generally falls across the segments. The author also calculates 99th-percentile absolute and relative changes.
A principal component analysis finds that the first component explains over half of the observed variation and has positive loadings across tenors; the first four together explain nearly all of it. The author proposes shocking these components and mapping the shocks back to tenor rates, but asks how to interpret the resulting scenarios and accommodate differing volatility levels. The only response points to a paper on learning curve dynamics with neural networks. It supplies no stress construction, validation, or interpretation, so the practical method remains unresolved.
Key ideas
- The curve is divided into short, medium, and long maturity segments with differing volatility behavior.
- The shortest tenor is reported as more volatile than nearby short maturities.
- The first four principal components explain nearly all variation in the sample, according to the author.
- Shifting principal components and reconstructing tenor changes is proposed but not explained or validated.
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Full text
# stress testing zero coupon yield curve # stress testing zero coupon yield curve i'm currently trying to stress test the zero coupon yield curve using daily observations from 2003 to 2019. Each Zero coupon yield curve originate from an actuarial curve with 37 tenors that range between 1 day and 30 years. the 1 day actuarial rate is the weighted average rate in interbank money market. As for the other tenors,they're calculated by linear interpolation of weighted average rate from treasury bond's secondary market. I divided the yield curve into 3 segments :short tenors(less than 1year) mid tenors (2y to 15y) long tenors (16y to 30y) The tenors in every segment have similar tendencies over time. I calculated the yields relative and absolute changes and i've noticed the following: - the one day yield is very volatile compared with other short tenors (7d,1m,2m ..) 2.the volatility decreases with segments Since we're in a low rate enviromnent, we're intrested by the rates tendency to increase. I've already calculated the 99% quantile for absolute and relative changes for every tenors but how can i apply them to reflect different levels of volatility. I also did a principal component analysis PCA and i found that the first axe explains 56% of my data and it's the only one with all positive coordinate.The first four axe explain 98%. i entend to apply shifts on the 4 PC and reverse the process to find the original tenors.but i don't know how to interpret the results. I'm looking for a way to capture different level of volatility in my yirld curve. ## Answer by CatFather (score -1) https://quant.stackexchange.com/a/45423 you might be interested in this: Learning Curve Dynamics with Artificial Neural Networks https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3041232
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