Bootstrapping PCA Yield-Curve Simulations for PRIIPs
Summary
The discussion outlines a proposed workflow for simulating yield-curve paths under a PRIIPs category 3 framework. After computing a yield-change matrix, principal component analysis is used to represent the curve’s movements through its main dimensions. The answer then describes resampling historical, smoothed returns by maturity for each future period, transforming simulated log returns back into yield levels, and reversing a nonnegativity adjustment applied earlier.
The material is explicitly an interpretation of the procedure, not a complete implementation guide. The questioner is uncertain about the later steps for zero-coupon bonds, discounting spreads, and aligning simulated tenor values with expectations at the end of the recommended holding period. A further reply offers one interpretation of that alignment adjustment, while acknowledging its conceptual uncertainty. Readers should therefore treat the resampling and adjustment sequence as a tentative reading of the regulatory method and verify the prescribed details before applying it.
Key ideas
- PCA can reduce yield-curve changes to a smaller set of principal dimensions before simulation.
- The proposed simulation resamples historical curve returns across maturities for successive future periods.
- Simulated log returns are converted back into yield levels, followed by reversal of a prior nonnegativity adjustment.
- The discussion leaves important implementation questions unresolved, including bond discounting and matching expected tenor values.
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# Simulation curves; PRIIPS category 3 # Simulation curves; PRIIPS category 3 Once the yield matrix has been computed, the eigenvectors must be calculated to project the yield matrix on the 3 main dimensions. Tehen is wasted to calculate the yield matrix to be used for the simulation. Until this point is clear, but in the next phase I can not understand how the simulation is performed. Can you know what steps are needed to simulate? I tried searching on the internet but I can not find clear and precise information about it. Thank you for availability ## Answer by Matúš Košík (score 0, accepted) https://quant.stackexchange.com/a/36995 As I understand it, using PCA you just "smoothen" the yield curve returns. Afterwards you bootstrap (pick random day from smoothened returns matrix and take this return at each maturity) every period in the future (if you have daily data = bootstrap return each day until maturity). This way you obtain random curve development until maturity and since the the returns are logarithms, you just take exponential of these simulated returns and multiply by the last observed yield (annex II point 23 b ii). Then you subtract the adjustment regarding nonnegativity that was applied in point 23 a ii. However what to do next, I am not sure. In my case, I have zero-bond. I am not sure what data to use, what spread to use when discounting. I was hoping there will be an example calculation done by EIOPA by now. ## Answer by el_george (score 0) https://quant.stackexchange.com/a/37034 My interpretation of what to do next regarding the point : "-adjusted so that the expected mean matches current expectations for the rate at tenor point T, at the end of the recommended holding period." is to subtract the current value of each tenor from each simulated tenor and add back the current expectation of the value of that tenor at the point in time where your simulated data refer. Adjusting each tenor point so that the expected value of the simulated tenor matches the current expectation of that tenor at the end of the RHP would not have any physical meaning to me. I am curious about your thoughts...
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