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On the Impact of Feeding Cost Risk in Aquaculture Valuation and Decision Making

Christian Oliver Ewald, Kevin Kamm

TL;DR

This work addresses how stochastic feeding costs affect aquaculture valuation and harvest timing by modeling salmon and feed markets with two independent Schwartz-2-factor dynamics under a risk-neutral framework. It compares optimal stopping rules derived under deterministic versus stochastic feeding costs using Least-Squares Monte Carlo and a Deep Optimal Stopping Network to learn the exercise boundary, and calibrates the model with two methods (Kalman filter and Cortazar nested LS), revealing notable model uncertainty. The main contributions are quantifying when feed-cost risk matters, demonstrating up to ~11.6% relative gains in high-volatility regimes, and showing that a DNN-based boundary learning approach scales to higher dimensions and provides robust stopping rules. The practical impact lies in guiding aquaculture investors on when to hedge feeding-cost risk, improving real-option valuation, and offering a computationally efficient framework for integrating feed-cost risk into decision-making.

Abstract

We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model. We compare the decision of harvesting salmon using a decision rule assuming either deterministic or stochastic feeding costs, i.e. including feeding cost risk. We identify cases, where accounting for stochastic feeding costs leads to significant improvements as well as cases where deterministic feeding costs are a good enough proxy. Nevertheless, in all of these cases, the newly derived rules show superior performance, while the additional computational costs are negligible. From a methodological point of view, we demonstrate how to use Deep-Neural-Networks to infer on the decision boundary that determines harvesting or continuation, improving on more classical regression-based and curve-fitting methods. To achieve this we use a deep classifier, which not only improves on previous results but also scales well for higher dimensional problems, and in addition mitigates effects due to model uncertainty, which we identify in this article. effects due to model uncertainty, which we identify in this article.

On the Impact of Feeding Cost Risk in Aquaculture Valuation and Decision Making

TL;DR

This work addresses how stochastic feeding costs affect aquaculture valuation and harvest timing by modeling salmon and feed markets with two independent Schwartz-2-factor dynamics under a risk-neutral framework. It compares optimal stopping rules derived under deterministic versus stochastic feeding costs using Least-Squares Monte Carlo and a Deep Optimal Stopping Network to learn the exercise boundary, and calibrates the model with two methods (Kalman filter and Cortazar nested LS), revealing notable model uncertainty. The main contributions are quantifying when feed-cost risk matters, demonstrating up to ~11.6% relative gains in high-volatility regimes, and showing that a DNN-based boundary learning approach scales to higher dimensions and provides robust stopping rules. The practical impact lies in guiding aquaculture investors on when to hedge feeding-cost risk, improving real-option valuation, and offering a computationally efficient framework for integrating feed-cost risk into decision-making.

Abstract

We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model. We compare the decision of harvesting salmon using a decision rule assuming either deterministic or stochastic feeding costs, i.e. including feeding cost risk. We identify cases, where accounting for stochastic feeding costs leads to significant improvements as well as cases where deterministic feeding costs are a good enough proxy. Nevertheless, in all of these cases, the newly derived rules show superior performance, while the additional computational costs are negligible. From a methodological point of view, we demonstrate how to use Deep-Neural-Networks to infer on the decision boundary that determines harvesting or continuation, improving on more classical regression-based and curve-fitting methods. To achieve this we use a deep classifier, which not only improves on previous results but also scales well for higher dimensional problems, and in addition mitigates effects due to model uncertainty, which we identify in this article. effects due to model uncertainty, which we identify in this article.
Paper Structure (10 sections, 20 equations, 3 figures, 6 tables)

This paper contains 10 sections, 20 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Mathematical Model and Framework
  3. Salmon Farm Parameters
  4. Optimal Stopping Problem
  5. Numerical Experiments
  6. Market Data
  7. Calibration to Market Data
  8. Comparison of Exercise Decisions
  9. Results
  10. Conclusion

Figures (3)

  • Figure 1: Interpolated (nearest neighbour) market future surfaces for salmon (left) and soy (right) from 01/01/2006 till 01/01/2023. On the $x$-axis are dates identified by integers, on the $y$-axis the time-to-maturity and on the $z$-axis the corresponding price. Deep blue associates a low and yellow a high price.
  • Figure 2: Close spot and future prices for different model parameters.
  • Figure 3: Mean relative changes of salmon (left) and soy (right) prices for the different scenarios in \ref{['tab:paramSalmon']}--\ref{['tab:paramSoy']}.

Theorems & Definitions (2)

  • Remark 2.1
  • Remark 3.1