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Joint risk-neutral laws and hedging

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  • Dilip Madan

Abstract

Complex positions on multiple underliers are hedged using the options surface of all underliers. Hedging objectives minimize ask prices for which post-hedge residual risks are acceptable at prespecified levels. It is shown that such hedges require the use of a risk-neutral law on the set of underlying risks. A joint risk-neutral law for multiple underliers is proposed and estimated from multiple option surfaces. Under the proposed joint law, asset returns are a linear mixture of independent Lévy components. Data on the independent components are estimated by an application of independent components analysis on time series data for the underlying returns. A comparison of the the risk-neutral law with the statistical law shows that risk neutral correlations dominate their statistical counterparts. Hedges significantly reduce ask prices.

Suggested Citation

  • Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:12:p:840-850
    DOI: 10.1080/0740817X.2010.541179
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    9. Ernst Eberlein & Dilip B. Madan, 2009. "Hedge Fund Performance: Sources And Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 267-282.
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    16. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
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    Cited by:

    1. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    2. Carr, Peter & Madan, Dilip B. & Melamed, Michael & Schoutens, Wim, 2016. "Hedging insurance books," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 364-372.
    3. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    4. Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
    5. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.

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