Aims

The aim of the research is to extend principal component analysis (PCA) of interest rates to use a bayesian framework.

Solvency UK and Classical PCA

Under Solvency UK many life insurers model 1 year movement in yield curve using PCA. The classical model is a dimensionality reduction technique. In practice this means that that movements across yield curve, at say 50 different terms, dont need to be modelled using 50 separate random variables but instead can be modelled using only say 3 principal components.

Purpose of introducing bayesian framework

The purpose of introducing a Bayesian framework is that it should enable the systematic inclusion of expert judgements i.e. views about the future dynamics of the process that are not in the historical data. It is suspected that general practice within the industry is to do this in an ad-hoc way, and not to use a systematic approach like Bayesian framework. Incorporating expert-informed priors can improve forecasts when changes in the economic environment are not yet reflected in the historical data.

Intended shape of this analysis

current plan

• Classical PCA an overview
• Bayesian PCA an overview
• Comparing Output using uninformative priors on the Bayesian PCA — see What Would Success Look Like? for what that means concretely for the latent track

The 4th aim is dependent on how well progressing and what is achievable within timeframe:

• a hierarchial model that has a prior predictive distribution that models dynamics of the process + (ideally) an informative prior of the parameters of the prior predicitve distribution that allows for economic judgements

the practitioner has to ask themselves, what real world beliefs about the yield curve am i confident to encode mathematically

or

Just informative prior on pure bayesian PCA model but this cannot be economic, just structural on the PCA asepct

Concluding with some brief thoughts on areas we are going to explore over the next 12 months.