Paper: arXiv 2603.17151

Authors: Jimin Lin

Abstract

Option prices encode the market’s collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter to rule out static arbitrage. Despite earlier recognition of their parity, the two had been studied in isolation for decades until the recent demand in implied volatility modeling rejuvenated such parity. This paper provides a systematic approach to build neural representations of option implied information. As a preliminary, we first revisit the explicit link between implied density and implied volatility through an alternative and minimalist lens, where implied volatility is viewed not as volatility but as a pointwise corrector mapping the Black-Scholes quasi-density into the implied risk-neutral density. Building on this perspective, we propose the neural representation that incorporates arbitrage constraints through the differentiable corrector. With an additive logistic model as the synthetic benchmark, extensive experiments reveal that deeper or wider network structures do not necessarily improve the model performance due to the nonlinearity of both arbitrage constraints and neural derivatives. By contrast, a shallow feedforward network with a single hidden layer and a specific activation effectively approximates implied density and implied volatility.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a clever re-framing of implied volatility as a pointwise corrector for Black-Scholes quasi-density, incorporating static arbitrage constraints directly into a neural network. Empirical tests on a synthetic benchmark demonstrate that shallow networks surprisingly outperform deeper architectures due to derivative non-linearities, providing a valuable methodological insight for option surface modeling.

Research Flowchart

  flowchart TD
    A[Goal: Neural Representation of Option Implied Info without Static Arbitrage] --> B[Revisit Link: View Implied Volatility as Pointwise Corrector]
    B --> C[Inputs: Black-Scholes Quasi-Density & Additive Logistic Benchmark]
    C --> D[Model Design: Incorporate Arbitrage Constraints via Differentiable Corrector]
    D --> E[Experiments: Compare Shallow vs. Deep/Wide Neural Architectures]
    E --> F[Outcome: Shallow Network with Single Hidden Layer Effectively Approximates Implied Volatility & Density]

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3 of 72 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.