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Quantitative White Papers.
These research white papers are detailed analyses that inform various elements of Kaiko’s data offerings. They’re independently published and backed by scientifically rigorous testing and peer-reviewed methodologies.
- On the simulation of extreme events with neural networks
M.Allouche, S.Girard and E.Gobet. Chapman & Hall/CRC, 2026
This work aims at investigating the use of generative methods based on neural networks to simulate extreme events.
See the white paper - ExcessGAN: simulation above extreme thresholds using Generative Adversarial Networks
M.Allouche, S.Girard and E.Gobet. Extremes, 2026
A neural network generative model for sampling multivariate data exceeding large thresholds.
See the white paper - Wilks confidence regions for empirical weighted quantiles
M.Allouche and E.Gobet. Statistics & Probability Letters, 2026
A data-based methodology is developed for estimating confidence intervals of weighted quantiles which naturally arise when aggregating fragmented price and volume data across multiple crypto-asset platforms. However, due to significant intra- and inter-platform variability, there is no single unique aggregated price. As a result, constructing confidence intervals is essential to properly quantify the uncertainty of the resulting aggregated price and, for data providers, to deliver more informative signals to market participants.
See the white paper - Statistical error bounds for weighted mean and median, with application to robust aggregation of cryptocurrency data
M.Allouche, M.Echenim, E.Gobet and A.C. Maurice. Mathematical Finance, 2025
Price aggregation methodologies applied to crypto-currency prices with quotations fragmented on different platforms are studied. An intrinsic difficulty is that the price returns and volumes are heavy-tailed, with many outliers, making averaging and aggregation challenging. While conventional methods rely on volume-weighted average prices (called VWAPs), or volume-weighted median prices (called VWMs), a new robust weighted median (RWM) estimator is developed that is robust to price and volume outliers.
See the white paper - Uniswap V3: Impermanent Loss Modeling and Swap Fees Asymptotic Analysis
M.Echenim, E.Gobet and A.C. Maurice. Submitted, 2025
A thorough analysis of Uniswap v3, forms part of the methodology for our Uniswap v3 data in our Level 1 & Level 2 Data subscriptions.
See the white paper - Modeling the risks within the protocol Aave, with an application to portfolio allocation
M.Echenim, E.Gobet and A.C. Maurice. Submitted, 2025
A detailed formalization of Aave’s lending, borrowing, and liquidation mechanisms, grounded in the protocol’s open-source implementation.
See the white paper - Optimal exit from Uniswap v3 and best expected return for a liquidity provider
A.Agarwal and E.Gobet. Submitted, 2025
Analysis of the profitability of liquidity providers’ positions in Uniswap v3 by aggregating fee income and impermanent loss within an optimal stopping framework.
See the white paper - Learning extreme Expected Shortfall and Conditional Tail Moments with neural networks. Application to cryptocurrency data
M.Allouche, S.Girard and E.Gobet. Neural Networks, 2024
A neural networks method is proposed to estimate extreme Expected Shortfall, and even more generally, extreme conditional tail moments as functions of confidence levels, in heavy-tailed settings.
See the white paper - Reduced-bias estimation of the extreme conditional tail expectation for Box-Cox transforms of heavy-tailed distributions
M.Allouche, J. El Methni and S.Girard. Journal of Statistical Planning and Inference, 2024
Reduced-bias estimators of the conditional tail expectation (a coherent risk measure) are introduced at intermediate and extreme levels for Box-Cox transformed heavy-tailed random variables.
See the white paper - Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes
M. Echenim, E. Gobet and A.C. Maurice. Quantitative Finance, 2023
A novel calibration procedure is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. This calibration procedure is shown to be significantly more robust and accurate than the ordinary one based on trade and mid-prices.
See the white paper