Replicating Portfolio Approach to Capital Calculation

32 Pages Posted: 13 Apr 2016 Last revised: 21 Oct 2017

See all articles by Mathieu Cambou

Mathieu Cambou

Ecole Polytechnique Fédérale de Lausanne

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Date Written: October 20, 2017

Abstract

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset-liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.

Keywords: Asset-Liability Portfolio, Chaos Expansion, Replicating Portfolio, Solvency Capital

JEL Classification: C61, C63, D81, G22

Suggested Citation

Cambou, Mathieu and Filipovic, Damir, Replicating Portfolio Approach to Capital Calculation (October 20, 2017). Finance Stochastics, Forthcoming; Swiss Finance Institute Research Paper No. 16-25. Available at SSRN: https://ssrn.com/abstract=2763733 or http://dx.doi.org/10.2139/ssrn.2763733

Mathieu Cambou

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Odyssea 1.04
1015 Lausanne, CH-1015
Switzerland

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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