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Constrained Polynomial Likelihood

Author

Listed:
  • Caio Almeida

    (Princeton University)

  • Paul Schneider

    (University of Lugano - Institute of Finance; Swiss Finance Institute)

Abstract

We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The PLR converges to the true, unknown, likelihood ratio. We show consistency, obtain the asymptotic distribution for the PLR coefficients estimated with sample moments, and present two applications. The first develops a PLR for the unknown transition density of a jump-diffusion process. The second modifies the Hansen-Jagannathan pricing kernel framework to accommodate polynomial return models consistent with no-arbitrage while simultaneously nesting the linear return model. In the S\&P 500 market, this modification entails sizable positions in option contracts necessary to implement the optimal trading strategy suggested by its dual portfolio formulation.

Suggested Citation

  • Caio Almeida & Paul Schneider, 2021. "Constrained Polynomial Likelihood," Swiss Finance Institute Research Paper Series 21-45, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2145
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    More about this item

    Keywords

    Likelihood ratio; positive polynomial; Reproducing Kernel Hilbert Space (RKHS);
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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