Contents

• Potential Questions that could be asked at Conference
• Bayesian method is for sparse noisy data but gilt yields abundant
• Regulation discourages novel approaches
• Slide 1
• Slide 2
• Slide 3
• Slide 4

Potential Questions that could be asked at Conference

• choice of dataset can be a concern: does framework help with choice of dataset
• are stresses multiplicative or additive in relation to current level of yield curve
• can data be amended to allow for features or can this approach prevent that
• application towards time-evolving stochastic model Ans: no, pca does not model time evolution
• types of prior that could be incorporated
• allowance for different datasets
• a lower bound below which stresses cannot go
• allowing for different dynamics at terms 1 and 2
• a belief that interest rate volatility will be higher/lower over coming year
• removal of drift eg long term downward drift seen prior to covid
• the yield curve will have a parallel downward shift of 30bps with probability 30%
• a prior that says in 1 years time the yield curve will make precisely a parallel shift likely generates a zero likelihood... i think the parameter values need to be able to express all of the history although maybe error terms in the probablistic model give us more flexibility.
• the prior likely needs be continuous
• normal, beta, log-normal distributions weight heavily weight preferred regions but don't exclude others

arbitrage * https://proteusllp.com/ArbitrageInRealWorld-Proteus.pdf

bayesian method is for sparse noisy data but gilt yields abundant

regulation discourages novel approaches

We are looking at merits of model in its own right
things that may appeal to regulation are systematisation of expert judgements

Slide 1

10. you mentioned transforming the dataset. does that involve standardisation ? standardisation is commonly used in principal component analysis when it makes sense to do so i.e. ?? different units ?? . But in our case we are comparing basis points to basis points.
    If you standardise ??i.e. run on a correlation matrix rather than a covariance matrix ?? (?? is that how a correlation matrix is created then ... by standardising data then a covariance matrix... i thought it was a different equation thoug ??)
    what happens if you do use correlation matrix, you effectively say that 3 month tenor moves around just as much as the 30 year yield, whereas we want to preserve the bps variance structure.
    Arguments for correlation if bringing in other data such as equity volatility of FX volatility where units are different.

17. why take logarithms?

18. used when you want changes in to be proportional to rather than absolute

19. volatility is proportional to level of rates
20. argument against logs: cannot take log of a negative

21. Lardic, Priaulet & Priaulet (2003), "PCA of the yield curve dynamics: questions of methodologies," Journal of Bond Trading and Management.

22. there may be a point that if propotional to the level rather than absolute we get higher explanatory power... i may sensitivity test this.

18. Using covariance because:

• ...??? reflect actual magnitude and not correlation structure only ??

• Lardic, Priaulet & Priaulet (2003), "PCA of the yield curve dynamics: questions of methodologies," Journal of Bond Trading and Management.

Slide 2

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Slide 3

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Slide 4

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what sort of no arbitrage constraints ?

• some yield curve shapes can admit arbitrate and therefore desirable to exclude them
• negative forward rates
• violation of monotonicity in discount factors

For example in the chart below : normal, inverted, humped are all legitimate the arbitrage one zig zags so vigourously that adjacent discount factors are not monotonically decreasing. * would PCA generate something like this zig zag though...

1. ssds
10. 50.