Pricing Kernel (Non) Monotonicity and Conditional Information
Speaker：Wolfgang Karl Härdle, Professor, Humboldt University of Berlin
Host：Kang Junqing, Associate Professor, Lingnan College
Time and Date：14:30, March 12, 2026 (Thursday)
Venue：W.T.Chan Auditorium (302), Lingnan Hall
Language：English + Chinese
Abstract：
Estimation of pricing kernels has received substantial attention, particularly following the emergence of the so-called "pricing kernel (PK) puzzle". Empirical PKs often differ from their theoretical counterparts because the theoretical PK is derived under the risk-neutral measure using a full forward-looking information set, whereas empirical estimates under the physical measure rely only on historical data. A newly proposed Conditional Density Integration (CDI) estimator, designed to reflect forward-looking information sets, aims to produce PKs that align with theory compatible PKs. However, we find that CDI does not fully resolve the issue, because when we compare CDI-estimated PKs with those from traditional methods, both still produce non-monotonic shapes that violate theoretical requirements. One further finding is that the desired monotonicity is highly dependent on the assumption of constant market volatility. The dependency on smoothing parameters further challenges the monotonicity-compliant PK. Empirical tests using S&P 500 and Bitcoin options confirm the impacts of volatility jumps on monotonicity of PK. Our study provides detailed insights into the limitation of PK estimation, which highlights stability of any PK estimations.
Profile:
Wolfgang Karl Härdle is the Ladislaus von Bortkiewicz Professor of Statistics at the Faculty of Business and Economics, Humboldt University of Berlin. His main research areas include quantitative finance, multivariate statistical analysis, explainable artificial intelligence, and computational statistical methods. Professor Härdle has authored, edited, or translated more than forty books and has published over 300 papers in leading journals in statistics and economics, including Econometrica, the Journal of the Royal Statistical Society, and the Journal of Econometrics. In terms of academic impact, his Google Scholar H-index is 92, the highest at Humboldt University of Berlin. He currently serves as Editor-in-Chief of Digital Finance and the Handbook of Computational Statistics.
Professor Härdle is the founder of the Blockchain Research Center (BRC). He previously managed the Collaborative Research Center CRC649 "Economic Risk" (2005–2016) and served as the principal investigator of the Sino-German joint research program IRTG1792 "High-Dimensional Non-Stationary Time Series Analysis" (2013–2023). He is also the founder of the Institute for Digital Assets at the Bucharest University of Economic Studies in Romania; the leader of the blockchain working group of the Marie Skłodowska-Curie Actions (MSCA) "DIGITAL" project; a member of the Board of Directors of AIFM Royalton Partners in Luxembourg; and a Huawei Distinguished Visiting Professor at the University of Edinburgh.
Professor Härdle is well known for pioneering research directions. He invented the "Quantlet and Quantinar" (Q2) ecosystem, which promotes academic collaboration and enhances transparency, reproducibility, and overall quality in scientific research.
