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Portfolio insurance under rough volatility and Volterra processes

Author

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  • Dupret, Jean-Loup

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model for which widely-used calibration techniques have long been known, as well as the rough Heston model which has garnered lots of attention from academicians and practitioners since 2014. The aim of this work is therefore to revisit and generalize the constant propotion portfolio insurance (CPPI) under the class of affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to affine Volterra processes, in particular when the variance process of the underlying risky asset is non-Markovian in the current variance state (as in the rough Heston model). We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of affine Volterra processes compared with classical simulation techniques. Using such approach, we describe in this paper several properties of CPPI (moments, density and risk measures), which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider different behaviors and more complex dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are extremely tractable and consistent with financial data.

Suggested Citation

  • Dupret, Jean-Loup & Hainaut, Donatien, 2021. "Portfolio insurance under rough volatility and Volterra processes," LIDAM Discussion Papers ISBA 2021026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  • Handle: RePEc:aiz:louvad:2021026
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    References listed on IDEAS

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    Cited by:

    1. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "A fractional Hawkes process for illiquidity modeling," LIDAM Discussion Papers ISBA 2023001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Hainaut, Donatien, 2022. "Pricing of spread and exchange options in a rough jump-diffusion market," LIDAM Discussion Papers ISBA 2022012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Hainaut, Donatien, 2022. "Multivariate rough claim processes: properties and estimation," LIDAM Discussion Papers ISBA 2022002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.

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    Keywords

    Finance ; Portfolio insurance ; CPPI ; Volterra processes ; Rough volatility;
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