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Alternative to beta coefficients in the context of diffusions

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  • Guillaume Bernis
  • Simone Scotti

Abstract

We develop an alternative to the beta coefficient of the CAPM theory. We show the link between this notion and the Wiener chaos expansion of the underlying processes. In the setting of Markov diffusions, we define the drift-neutral beta, which is the quantity of benchmark such that the resulting portfolio is immune to an infinitesimal change of drift on the Brownian motion driving the benchmark. Our approach yields a coefficient which in many practical cases depends on the initial values of both the portfolio and its benchmark. It can also be used to take into account extreme risks and not only the variance. We study several classical diffusion processes and give a full analysis in the case of Jacobi processes. Examples with credit indices show the efficiency of the method in hedging a portfolio.

Suggested Citation

  • Guillaume Bernis & Simone Scotti, 2017. "Alternative to beta coefficients in the context of diffusions," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 275-288, February.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:2:p:275-288
    DOI: 10.1080/14697688.2016.1188214
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    References listed on IDEAS

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    1. Lane Hughston & Avraam Rafailidis, 2005. "A chaotic approach to interest rate modelling," Finance and Stochastics, Springer, vol. 9(1), pages 43-65, January.
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    Cited by:

    1. Michele Bonollo & Luca Di Persio & Luca Mammi & Immacolata Oliva, 2017. "Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time," Papers 1704.03244, arXiv.org.
    2. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    3. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.

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