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Robust Stochastic Discount Factors

Author

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  • Phelim Boyle
  • Shui Feng
  • Weidong Tian
  • Tan Wang

Abstract

When the market is incomplete, a new non-redundant derivative security cannot be priced by no-arbitrage arguments alone. Moreover, there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new derivative security. This paper develops an approach to the selection of a stochastic discount factor for pricing a new derivative security. The approach is based on the idea that the price of a derivative security should not vary too much when the payoff of the primitive security is slightly perturbed, i.e., the price of the derivative should be robust to model misspecification. The paper develops two metrics of robustness. The first is based on robustness in expectation. The second is based on robustness in probability and draws on tools from the theory of large deviations. We show that in a stochastic volatility model, the two metrics yield analytically tractable bounds for the derivative price, as the underlying stochastic volatility model is perturbed. The bounds can be readily used for numerical examination of the sensitivity of the price of the derivative to model misspecification. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

Suggested Citation

  • Phelim Boyle & Shui Feng & Weidong Tian & Tan Wang, 2008. "Robust Stochastic Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1077-1122, May.
    • Handle: RePEc:oup:rfinst:v:21:y:2008:i:3:p:1077-1122
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    File URL: http://hdl.handle.net/10.1093/rfs/hhm067
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    Cited by:

    1. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.
    2. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    3. Nina Boyarchenko & Mario Cerrato & John Crosby & Stewart Hodges, 2012. "No good deals—no bad models," Staff Reports 589, Federal Reserve Bank of New York.
    4. Chang-Chih Chen & Chia-Chien Chang, 2019. "How Big are the Ambiguity-Based Premiums on Mortgage Insurances?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(1), pages 133-157, January.
    5. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2016. "On the properties of the constrained Hansen–Jagannathan distance," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 121-150.
    6. Chen, Chang-Chih & Ho, Kung-Cheng & Yan, Cheng & Yeh, Chung-Ying & Yu, Min-Teh, 2023. "Does ambiguity matter for corporate debt financing? Theory and evidence," Journal of Corporate Finance, Elsevier, vol. 80(C).
    7. Ban, Mingyuan & Chen, Chang-Chih, 2019. "Ambiguity and capital structure adjustments," International Review of Economics & Finance, Elsevier, vol. 64(C), pages 242-270.
    8. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2010. "On the Hansen-Jagannathan distance with a no-arbitrage constraint," FRB Atlanta Working Paper 2010-04, Federal Reserve Bank of Atlanta.

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