RFS Advance Access published online on December 13, 2007
Review of Financial Studies, doi:10.1093/rfs/hhm067
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Robust Stochastic Discount Factors
Wilfrid Laurier University
McMaster University
University of Waterloo
University of British Columbia and CCFR
Address correspondence to Weidong Tian, Department of Statistics & Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1; e-mail: wdtian{at}uwaterloo.ca.
JEL Classification: G11, G12
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Abstract |
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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.
We are very grateful to the editor, Yacine Aït-Sahalia, and an anonymous referee for several constructive and insightful suggestions on how to improve the paper. We would like to acknowledge comments from George M. Constantinides, Jérôme Detemple, Jun Liu, Jiang Wang, Hong Yan, and participants at presentations given at McGill University, the University of Montreal, the University of British Columbia, the University of Florida, the University of Western Ontario, and the Third World Congress of the Bachelier Finance Society in Chicago. We are responsible for any errors. The authors thank the Natural Sciences and Engineering Research Council and the Social Sciences and Humanities Research Council for their support.