Extrapolation and generative algorithms for three applications in finance

TL;DR

The paper develops a unified kernel-RKHS framework for three central finance problems: pricing extrapolation, inverse (reverse) stress testing, and generative modeling of time series with conditioning. It combines reproducing kernel methods with optimal transport-inspired encoders/decoders and permutation-based sampling to map between market data, pricing outputs, and latent representations, enabling interpretable, data-efficient extrapolation and scenario generation. It demonstrates that offline learned pricing can be extrapolated to new dates with basis-point accuracy, enables reverse-stress testing through conditioned generators, and extends traditional models by conditioning on informative signals, including a GARCH-based time-series generator. The approach offers a computationally efficient, auditable path to real-time risk management and strategy benchmarking in finance.

Abstract

For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use cases are investigated. First, we show that extrapolating from few pricer examples leads to sufficiently accurate and computationally efficient results so that our algorithm can serve as a pricing framework. The second use case concerns reverse stress testing, which is formulated as an inversion function problem and is treated here via an optimal transport technique in combination with the notions of kernel-based encoders, decoders, and generators. Third, we show that standard techniques for time series analysis can be enhanced by using the proposed generative algorithms. Namely, we use our algorithm in order to extend the validity of any given quantitative model. Our approach allows for conditional analysis as well as for escaping the `Gaussian world'. This latter property is illustrated here with a portfolio investment strategy.

Figures (8)

• Figure 1: Charts for Apple, Amazon, and Google
• Figure 2: Payoff (left), and pricer (right) values
• Figure 3: A benchmark of PnL extrapolation methods
• Figure 4: A benchmark of PnL greeks from an extrapolation methods
• Figure 5: Reverse prices (left) and benchmark (right)