Characteristics of Model-Free Pricing Kernels

41 Pages Posted: 9 Jan 2021

See all articles by Maxim Ulrich

Maxim Ulrich

Karlsruhe Institute of Technology

Simon Walther

Karlsruhe Institute of Technology; Universal-Investment-Luxembourg S.A. Niederlassung Frankfurt am Main

Date Written: April 16, 2020

Abstract

This study combines model-free conditional estimators for the risk-neutral and the physical distribution of equity returns to obtain daily measures for the pricing kernel at the monthly time horizon. Despite their time-varying nature, our pricing kernels are non-parametric, forward-looking, agnostic about preferences, economic state variables or their dynamics and rely only on minimal technical constraints. Still, our realized pricing kernel estimates are clearly linked to economic state variables like the term spread, the credit spread or liquidity. We decompose the expected variance of the log pricing kernel and find that jumps contribute a considerable portion to overall pricing kernel risk. Building on statistical tests, we confirm an U-shape in the pricing kernel at all times and find a strong link between variations in its magnitude and the variance risk premium. A central hump in the pricing kernel can be confirmed unconditionally, but appears to fade during crisis times.

Keywords: pricing kernel, model-free, density estimator, neural networks

Suggested Citation

Ulrich, Maxim and Walther, Simon, Characteristics of Model-Free Pricing Kernels (April 16, 2020). Available at SSRN: https://ssrn.com/abstract=3733838 or http://dx.doi.org/10.2139/ssrn.3733838

Maxim Ulrich

Karlsruhe Institute of Technology ( email )

Bluecherstrasse 17
Karlsruhe, Baden W├╝rttemberg 76131
Germany
+4972160844270 (Phone)

HOME PAGE: http://risk.fbv.kit.edu/c-ram

Simon Walther (Contact Author)

Karlsruhe Institute of Technology ( email )

Bluecherstrasse 17
Karlsruhe, Baden W├╝rttemberg 76131
Germany

Universal-Investment-Luxembourg S.A. Niederlassung Frankfurt am Main ( email )

Theodor-Heuss-Allee 70
Frankfurt am Main, 60486
Germany

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