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Replicating portfolio approach to capital calculation

Author

Listed:
  • Mathieu Cambou

    (Institute of Mathematics)

  • Damir Filipović

    (Swiss Finance Institute)

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.

Suggested Citation

  • Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0347-1
    DOI: 10.1007/s00780-017-0347-1
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    Cited by:

    1. Patrick Cheridito & John Ery & Mario V. Wuthrich, 2021. "Assessing asset-liability risk with neural networks," Papers 2105.12432, arXiv.org.
    2. Lotfi Boudabsa & Damir Filipović, 2022. "Machine learning with kernels for portfolio valuation and risk management," Finance and Stochastics, Springer, vol. 26(2), pages 131-172, April.
    3. Jesse M. Keenan & Anurag Gumber, 2019. "California climate adaptation trust fund: exploring the leveraging of cap-and-trade proceeds," Environment Systems and Decisions, Springer, vol. 39(4), pages 454-465, December.
    4. Patrick Cheridito & John Ery & Mario V. Wüthrich, 2020. "Assessing Asset-Liability Risk with Neural Networks," Risks, MDPI, vol. 8(1), pages 1-17, February.
    5. Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.
    6. Hampus Engsner & Kristoffer Lindensjo & Filip Lindskog, 2018. "The value of a liability cash flow in discrete time subject to capital requirements," Papers 1808.03328, arXiv.org.
    7. Hampus Engsner & Kristoffer Lindensjö & Filip Lindskog, 2020. "The value of a liability cash flow in discrete time subject to capital requirements," Finance and Stochastics, Springer, vol. 24(1), pages 125-167, January.

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    More about this item

    Keywords

    Asset–liability portfolio; Chaos expansion; Replicating portfolio; Solvency capital;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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