Transfer Learning (Il)liquidity

TL;DR

This paper introduces a novel neural network architecture that leverages transfer learning to accurately estimate the Risk Neutral Density from option prices, especially in illiquid markets with limited data.

Contribution

It proposes the Deep Log-Sum-Exp Neural Network, demonstrating its statistical properties and effectiveness in estimating RND under severe illiquidity, validated through simulations and empirical data.

Findings

Effective RND estimation with minimal data

Improved accuracy in illiquid market conditions

Statistical consistency of the proposed model

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.