Paper: arXiv 2409.06551

Abstract

The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global universal approximation theorem based on Barron-type estimates. The method is based on the specification of a prior distribution on the neural network weights and an adequately chosen likelihood function. The resulting posterior distribution can be seen as a mixture of different classical neural SDE models yielding robust bounds on the implied volatility surface. Both, historical financial time series data and option price data are taken into consideration, which necessitates a methodology to learn the change of measure between the risk-neutral and the historical measure. The key ingredient for a robust numerical optimization of the neural networks is to apply a Langevin-type algorithm, commonly used in the Bayesian approaches to draw posterior samples.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper involves advanced Bayesian methods, neural SDEs, universal approximation theorems, and measure change theory, indicating high mathematical density. However, the excerpt presents a proof-of-concept framework with sensitivity analysis but lacks detailed empirical results, code, or specific backtesting metrics.

Research Flowchart

  flowchart TD
  A["Research Goal: Robust Calibration of Financial Models"] --> B["Methodology: Bayesian Framework"]
  B --> C["Inputs: Options & Historical Data"]
  C --> D["Process: Measure Change & Neural SDE"]
  D --> E["Computation: Langevin Sampling"]
  E --> F["Outcomes: Robust Implied Vol. Bounds & Universal Approximation"]

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3 of 64 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.