# Option market trading activity and the estimation of the pricing kernel: A Bayesian approach

*Giovanni Barone-Adesi*,
*Nicola Fusari*,
*Antonietta Mira* and
*Carlo Sala*

*Journal of Econometrics*, 2020, vol. 216, issue 2, 430-449

**Abstract:**
We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the amount of trading activity in deep-out-of-the-money options. We use the option-adjusted physical measure to construct an option-adjusted pricing kernel. An empirical investigation on the S&P 500 Index from 2002 to 2015 shows that the option-adjusted pricing kernel is consistently monotonically decreasing, regardless of the level of volatility, thus providing an explanation to the well known U-shaped pricing kernel puzzle.

**Keywords:** Pricing kernel; Pricing kernel puzzle; Physical measure; Dirichlet process; Bayesian nonparametric estimation; Options; S&P 500 index (search for similar items in EconPapers)

**JEL-codes:** G10 G13 G14 G17 (search for similar items in EconPapers)

**Date:** 2020

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:216:y:2020:i:2:p:430-449

**DOI:** 10.1016/j.jeconom.2019.11.001

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