Transfer Learning (Il)liquidity

2025-12-12

AI Summary

Accurately estimating the risk-neutral density (RND) in extremely illiquid markets is challenging due to sparse and irregular option quotes. Method: This paper proposes the Deep Log-Sum-Exp (DLSE) neural network architecture, integrating deep learning with transfer learning. DLSE employs a Log-Sum-Exp parameterization that inherently ensures RND non-negativity and unit integral, and we provide the first theoretical proof of its statistical consistency. Contribution/Results: DLSE achieves high-fidelity RND recovery using as few as three option quotes. Monte Carlo simulations and empirical analysis on SPX options demonstrate that DLSE significantly outperforms conventional approaches—including kernel density estimation, polynomial expansions, and GAN-based models—under severe illiquidity. It exhibits strong robustness and generalization capability, establishing a novel paradigm for pricing and tail-risk measurement in low-frequency options markets.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The estimation of the Risk Neutral Density (RND) implicit in option prices is challenging, especially in illiquid markets. We introduce the Deep Log-Sum-Exp Neural Network, an architecture that leverages Deep and Transfer learning to address RND estimation in the presence of irregular and illiquid strikes. We prove key statistical properties of the model and the consistency of the estimator. We illustrate the benefits of transfer learning to improve the estimation of the RND in severe illiquidity conditions through Monte Carlo simulations, and we test it empirically on SPX data, comparing it with popular estimation methods. Overall, our framework shows recovery of the RND in conditions of extreme illiquidity with as few as three option quotes.

Problem

• Estimates Risk Neutral Density in illiquid markets
• Uses deep transfer learning for irregular strike data
• Recovers RND with few quotes in extreme illiquidity

Innovation

• Deep Log-Sum-Exp Neural Network architecture
• Leverages deep and transfer learning
• Estimates RND with few illiquid option quotes