Neural and Time-Series Approaches for Pricing Weather Derivatives: Performance and Regime Adaptation Using Satellite Data

Paper: arXiv 2411.12013

Abstract

This paper studies pricing of weather-derivative (WD) contracts on temperature and precipitation. For temperature-linked strangles in Toronto and Chicago, we benchmark a harmonic-regression/ARMA model against a feed-forward neural network (NN), finding that the NN reduces out-of-sample mean-squared error (MSE) and materially shifts December fair values relative to both the time-series model and the industry-standard Historic Burn Approach (HBA). For precipitation, we employ a compound Poisson–Gamma framework: shape and scale parameters are estimated via maximum likelihood estimation (MLE) and via a convolutional neural network (CNN) trained on 30-day rainfall sequences spanning multiple seasons. The CNN adaptively learns season-specific $(α,β)$ mappings, thereby capturing heterogeneity across regimes that static i.i.d.\ fits miss. At valuation, we assume days are i.i.d.\ $Γ(\hatα,\hatβ)$ within each regime and apply a mean-count approximation (replacing the Poisson count by its mean ($n\hatλ$) to derive closed-form strangle prices. Exploratory analysis of 1981–2023 NASA POWER data confirms pronounced seasonal heterogeneity in $(α,β)$ between summer and winter, demonstrating that static global fits are inadequate. Back-testing on Toronto and Chicago grids shows that our regime-adaptive CNN yields competitive valuations and underscores how model choice can shift strangle prices. Payoffs are evaluated analytically when possible and by simulation elsewhere, enabling a like-for-like comparison of forecasting and valuation methods.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics, including harmonic regression with ARMA models, compound Poisson–Gamma processes, MLE, and CNN architectures, with significant analytical derivations. It demonstrates strong empirical rigor through extensive back-testing on a 42-year satellite dataset (NASA POWER) for two cities, comparing models against industry benchmarks and reporting specific metrics like MSE and fair value shifts.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Price Weather Derivatives<br>Temperature & Precipitation"] --> B["Data Source:<br>NASA POWER 1981-2023"]
  
  subgraph C["Temperature Modeling: Toronto & Chicago"]
      B --> C1["Model 1: Time-Series<br>Harmonic Regression + ARMA"]
      B --> C2["Model 2: Neural Network<br>Feed-Forward NN"]
      C1 --> C3["Compare MSE & Fair Values"]
      C2 --> C3
  end

  subgraph D["Precipitation Modeling"]
      B --> D1["Base Model: Compound Poisson-Gamma<br>MLE Estimation"]
      B --> D2["Adaptive Model: CNN<br>Trained on 30-day Rainfall Sequences"]
      D2 --> D3["Learn Regime-Specific (α, β)<br>Summer vs Winter Heterogeneity"]
  end
  
  C3 --> E["Key Findings<br>NN reduces MSE vs Time-Series<br>Model choice shifts fair values<br>CNN captures precipitation regimes"]
  D3 --> E

Cited References (100)

1. Weather Derivatives: Modeling and Pricing Weather-Related Risk (2013)
2. Deep Learning for Time Series Forecasting Predict the Future with MLPs, CNNs and LSTMs in Python (2018)
3. An Introduction to Statistical Learning with Applictions in R (2013)
4. Hands-On Machine Learning with Scikit-Learn, Keras & TensorFlow Concepts, Tools, and Techniques to Build Intelligent Systems (2023)
5. Stochastic modelling of temperature variations with a view towards weather derivatives (2005)
6. Option valuation using the fast Fourier transform (1999)
7. Switching L 'e vy Models in Continuous Time: Finite Distributions and Option Pricing (2005)
8. A Novel Pricing Method for European Options based on Fourier-Cosine Series Expansions (2008)

0 of 100 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.