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Estimating a conditional density ratio model for asset returns and option demand

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  • Dalderop, Jeroen
  • Linton, Oliver

Abstract

Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, 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. We characterize the asymptotic bias and variance of the estimator and its multiplicatively corrected density forecasts. A local exponential linear variant is proposed to include conditioning variables. The estimator performs well in a simulation study, even when the risk-neutral densities are noisy and/or have missing tails. We apply our estimator to a demand-based model for S&P 500 index options, and find U-shaped pricing kernels when end-users sell out-of-the-money options and volatility is high.

Suggested Citation

  • Dalderop, Jeroen & Linton, Oliver, 2026. "Estimating a conditional density ratio model for asset returns and option demand," Journal of Econometrics, Elsevier, vol. 254(PB).
    • Handle: RePEc:eee:econom:v:254:y:2026:i:pb:s0304407626000126
    DOI: 10.1016/j.jeconom.2026.106191
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