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Multivariate Distributions For Financial Returns

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  • DILIP B. MADAN

    (Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA)

Abstract

Multivariate return distributions consistent with bilateral gamma marginals are formulated and termed multivariate bilateral gamma (MBG). Tail probability distances and Wasserstein distances between return data, model simulations and their squares evaluate the model performance. A full Gaussian copula (FGC) is taken as an alternate test model and the MBG delivers a comparatively better performance for equity pairs. The MBG is however inadequate for the S&P 500 index return when paired with the VIX returns. Applying MBG to the S&P 500 the index and regression residuals of VIX on the S&P 500 index return is successful. This model is termed MBGR. The residual taken as an independent bilateral gamma, delivers the model MBGIR. Characteristic function estimations are employed to develop asset-specific VIX levels and their joint returns with the asset return are studied. The CBOE SKEW index is generalized to be asset-specific and triples of returns for the asset, its VIX and its SKEW are studied using all four models and performance statistics. The model MBGR continues to deliver a good performance.

Suggested Citation

  • Dilip B. Madan, 2020. "Multivariate Distributions For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-32, September.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:06:n:s0219024920500417
    DOI: 10.1142/S0219024920500417
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    Citations

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    Cited by:

    1. Yoshihiro Shirai, 2023. "Acceptable Bilateral Gamma Parameters," Papers 2301.05333, arXiv.org.
    2. Dilip B. Madan & King Wang, 2021. "Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices," JRFM, MDPI, vol. 14(8), pages 1-20, August.
    3. Dilip B. Madan & King Wang, 2023. "The valuation of corporations: a derivative pricing perspective," Annals of Finance, Springer, vol. 19(1), pages 1-21, March.
    4. Yoshihiro Shirai, 2022. "Extreme Measures in Continuous Time Conic Finace," Papers 2210.13671, arXiv.org, revised Oct 2023.
    5. Maria Grazia Zoia & Gianmarco Vacca & Laura Barbieri, 2020. "Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions," Risks, MDPI, vol. 8(4), pages 1-21, November.
    6. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.

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