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Transfer Learning (Il)liquidity

Author

Listed:
  • Andrea Conti
  • Giacomo Morelli

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.

Suggested Citation

  • Andrea Conti & Giacomo Morelli, 2025. "Transfer Learning (Il)liquidity," Papers 2512.11731, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2512.11731
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    References listed on IDEAS

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    1. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
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