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Estimating a Density Ratio Model for Stock Market Risk and Option Demand

Author

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  • Dalderop, J.
  • Linton, O. B.

Abstract

Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, investor risk aversion introduces a multiplicative pricing kernel between the risk-neutral and true conditional densities of the underlying asset's return. This paper proposes a simple local estimator of the pricing kernel based on inverse density weighting, and characterizes its asymptotic bias and variance. The estimator can be used to correct biased density forecasts, and performs well in a simulation study. A local exponential linear variant of the estimator is proposed to include conditioning variables. In an application, we estimate a demand-based model for S&P 500 index options using net positions data, and attribute the U-shaped pricing kernel to heterogeneous beliefs about conditional volatility.

Suggested Citation

  • Dalderop, J. & Linton, O. B., 2024. "Estimating a Density Ratio Model for Stock Market Risk and Option Demand," Cambridge Working Papers in Economics 2411, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2411
    Note: obl20
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    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    2. Rui Albuquerque & Martin Eichenbaum & Victor Xi Luo & Sergio Rebelo, 2016. "Valuation Risk and Asset Pricing," Journal of Finance, American Finance Association, vol. 71(6), pages 2861-2904, December.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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