Principal component analysis of yield curve movements

Barber, Joel R.; Copper, Mark L.

doi:10.1007/s12197-010-9142-y

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…The first six components explain between 99.2 and 99.5% of the variance with a 90% confidence interval (cf. [ 5 ]). The principal components describe the different yield curve movements and the first three are interpreted as the shift, twist and butterfly moves of the yield curve [ 31 , 37 ].…”

Section: Appendix 1: Datamentioning

confidence: 99%

“…In this appendix, we describe the principal component analysis (PCA) to calibrate the interest rate shocks. PCA is used to describe movements of the yield curve and is explained by Fiori and Iannotti [ 27 ] and Barber and Copper [ 5 ]. It applies an orthogonal linear transformation that converts interest rate changes data of correlated variables into a set of values of linearly uncorrelated variables.…”

Section: Appendix 1: Datamentioning

confidence: 99%

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Solvency II solvency capital requirement for life insurance companies based on expected shortfall

Boonen

2017

Eur. Actuar. J.

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This paper examines the consequences for a life annuity insurance company if the solvency II solvency capital requirements (SCR) are calibrated based on expected shortfall (ES) instead of value-at-risk (VaR). We focus on the risk modules of the SCRs for the three risk classes equity risk, interest rate risk and longevity risk. The stress scenarios are determined using the calibration method proposed by EIOPA in 2014. We apply the stress-scenarios for these three risk classes to a fictitious life annuity insurance company. We find that for EIOPA’s current quantile 99.5% of the VaR, the stress scenarios of the various risk classes based on ES are close to the stress scenarios based on VaR. Might EIOPA choose to calibrate the stress scenarios on a smaller quantile, the longevity SCR is relatively larger and the equity SCR is relatively smaller if ES is used instead of VaR. We derive the same conclusion if stress scenarios are determined with empirical stress scenarios.

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Section: Appendix 1: Datamentioning

confidence: 99%

Section: Appendix 1: Datamentioning

confidence: 99%

Solvency II solvency capital requirement for life insurance companies based on expected shortfall

Boonen

2017

Eur. Actuar. J.

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“…4 The 5-year bond has 2.13% coupons, and the 30-year bond has 3.45% coupons. 5 We determine the bond portfolio as follows. The duration of the bonds equals 50% of the duration of the liabilities.…”

Section: Calibrating the Fictitious Life Annuity Insurermentioning

confidence: 99%

“…4 For EEA government bonds that have a AAA credit rating, an insurer is not required to hold an SCR for spread risk by EIOPA [21]. 5 The coupon rates are based on the 5-and 30-year UK Gilt bonds on December 31st, 2014. Therefore, to compare the SCR(VaR a ) properly with the SCR(ES h ), the confidence level for the ES, h, is chosen based on matching the reduced total SCR value, i.e.,…”

Section: Matching the Total Scr Valuementioning

confidence: 99%

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Solvency II Solvency Capital Requirement for Life Insurance Companies Based on Expected Shortfall

Boonen

2015

SSRN Journal

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This paper examines the consequences for a life annuity insurance company if the solvency II solvency capital requirements (SCR) are calibrated based on expected shortfall (ES) instead of value-at-risk (VaR). We focus on the risk modules of the SCRs for the three risk classes equity risk, interest rate risk and longevity risk. The stress scenarios are determined using the calibration method proposed by EIOPA in 2014. We apply the stress-scenarios for these three risk classes to a fictitious life annuity insurance company. We find that for EIOPA's current quantile 99.5% of the VaR, the stress scenarios of the various risk classes based on ES are close to the stress scenarios based on VaR. Might EIOPA choose to calibrate the stress scenarios on a smaller quantile, the longevity SCR is relatively larger and the equity SCR is relatively smaller if ES is used instead of VaR. We derive the same conclusion if stress scenarios are determined with empirical stress scenarios.

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Empirical analysis of term structure shifts

Barber

2020

J Econ Finan

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Principal component analysis and factor analysis of term structure movements shows that between 80 and 90% of term structure shifts can be explained by a uniform shift that is roughly parallel. In contrast, our analysis of term structure data from 1986 to 2016 reveals that only 57% of the shifts have been uniform. Twist-and butterflytype shifts accounted for 28 and 10%, respectively, of all shifts. Remarkably, these frequency results are roughly the same for uniform and twist shifts determined on a daily, weekly, and monthly basis over the entire sample and over three subperiods. Based on historical data, an investor should expect a uniform shift in the term structure about 57% and a twist 28% of the time. Keywords Term structure shift • Spot rates • Principal component analysis JEL Classification G12 1 Macaulay (1938) originated the concept of duration. Bierwag et al. (1983) provided an excellent survey of the literature. 2 The prices on zero coupon bond, from which the returns were calculated, are based on spot rates implied by in prices of coupon bonds.

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Principal component analysis of yield curve movements

Cited by 13 publications

References 11 publications

Solvency II solvency capital requirement for life insurance companies based on expected shortfall

Solvency II solvency capital requirement for life insurance companies based on expected shortfall

Solvency II Solvency Capital Requirement for Life Insurance Companies Based on Expected Shortfall

Empirical analysis of term structure shifts

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