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Monotonicity of the Stochastic Discount Factor and Expected Option Returns

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  • Ranadeb Chaudhuri
  • Mark Schroder

Abstract

Evidence shows that the stochastic discount factor (SDF) is not always a downward-sloping function of S&P 500 returns when estimated using options data. In contrast, our results suggest that SDFs as functions of individual stock returns are generally downward sloping. A simple jump-diffusion model can reconcile these empirical findings. The same model also implies a steeper implied-volatility curve for the index than for the typical stock, a well-known empirical fact from the options literature. Both the SDF and volatility-curve results can be explained by a common source of jump risk among stocks, together with diversification of Brownian risk in the index. We also devise novel empirical tests of SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the return density functions.

Suggested Citation

  • Ranadeb Chaudhuri & Mark Schroder, 2015. "Monotonicity of the Stochastic Discount Factor and Expected Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1462-1505.
    • Handle: RePEc:oup:rfinst:v:28:y:2015:i:5:p:1462-1505.
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    File URL: http://hdl.handle.net/10.1093/rfs/hhv011
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    Cited by:

    1. Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.
    2. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    3. Jiao, Yuhan & Liu, Qiang & Guo, Shuxin, 2021. "Pricing kernel monotonicity and term structure: Evidence from China," Journal of Banking & Finance, Elsevier, vol. 123(C).
    4. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    5. Jacobs, Kris & Li, Bingxin, 2023. "Option Returns, Risk Premiums, and Demand Pressure in Energy Markets," Journal of Banking & Finance, Elsevier, vol. 146(C).
    6. Nawalkha, Sanjay K & Zhuo, Xiaoyang, 2020. "A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims," OSF Preprints hsxtu, Center for Open Science.
    7. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    8. 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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