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Recovery with Unbounded Diffusion Processes

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  • Johan Walden

Abstract

We analyze the problem of recovering the pricing kernel and real probability distribution from observed option prices, when the state variable is an unbounded diffusion process. We derive necessary and sufficient conditions for recovery. In the general case, these conditions depend on the properties of the diffusion process, but not on the pricing kernel. We also show that the same conditions determine whether recovery works in practice, when the continuous problem is approximated on a bounded or discrete domain without further specification of boundary conditions. Altogether, our results suggest that recovery is possible for many interesting diffusion processes on unbounded domains.

Suggested Citation

  • Johan Walden, 2017. "Recovery with Unbounded Diffusion Processes," Review of Finance, European Finance Association, vol. 21(4), pages 1403-1444.
    • Handle: RePEc:oup:revfin:v:21:y:2017:i:4:p:1403-1444.
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    File URL: http://hdl.handle.net/10.1093/rof/rfw068
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
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    4. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
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    6. Jeff Hamrick & Murad Taqqu, 2009. "Testing diffusion processes for non-stationarity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 509-551, July.
    7. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.
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    Cited by:

    1. Jensen, Christian Skov & Lando, David & Pedersen, Lasse Heje, 2019. "Generalized recovery," Journal of Financial Economics, Elsevier, vol. 133(1), pages 154-174.
    2. Ngoc-Khanh Tran, 2019. "The Functional Stochastic Discount Factor," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 1-49, December.
    3. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    4. Hyungbin Park, 2018. "A representative agent model based on risk-neutral prices," Papers 1801.09315, arXiv.org.
    5. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    6. 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.
    7. Jackwerth, Jens Carsten & Menner, Marco, 2020. "Does the Ross recovery theorem work empirically?," Journal of Financial Economics, Elsevier, vol. 137(3), pages 723-739.

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    More about this item

    Keywords

    Recovery theorem; Ross recovery; Asset pricing;
    All these keywords.

    JEL classification:

    • 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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