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Functional Ross recovery: Theoretical results and empirical tests

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  • Dillschneider, Yannick
  • Maurer, Raimond

Abstract

Recently, Ross (2015) showed that the real-world probability distribution of a discrete Markovian state variable can be recovered from observed option prices. The so-called recovery theorem follows from Perron–Frobenius matrix theory when the pricing kernel is transition independent. In this paper, we generalize the recovery theorem to continuous state spaces using Perron–Frobenius operator theory. Building on our theoretical results, we devise a nonparametric approach to empirically estimate the recovered pricing kernel and probability density in closed form. Using S&P 500 index options, we analyze recovered pricing kernels empirically and find evidence that Ross recovery is misspecified.

Suggested Citation

  • Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:dyncon:v:108:y:2019:i:c:s0165188919301496
    DOI: 10.1016/j.jedc.2019.103750
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    1. Shinmi Ahn & Hyungbin Park, 2020. "Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    2. Sanford, Anthony, 2024. "Information content of option prices: Comparing analyst forecasts to option-based forecasts," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).

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    More about this item

    Keywords

    Ross recovery; Pricing kernel; State price density; Perron–Frobenius theory;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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