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Research · University of Amsterdam · Remote collaboration
Renewable Capture-Price Forecasting with Wasserstein Gaussian Processes
The capture price of wind or solar is the production-weighted average of the spot price over a delivery period. Its forecast depends on the covariance between price and production, so the joint forecast is treated as a probability measure and used as the input to a Gaussian process.
Paper
Open paper (PDF) ↗Timeline
- Outreach and scopingIndependent outreach on infinite-dimensional and Wasserstein-space GP methods led to a long-term collaboration. The joint direction was scoped as renewable capture-price forecasting.
- Synthetic validationWasserstein and Sinkhorn-kernel GP regression, with GP quantile-barycenter forecasting, tested on synthetic bivariate price–production models against moment-based and persistence baselines.
- Predictive-variance fixEmpirical coverage was far below nominal because the noise term was omitted from the predictive variance. Correcting it moved coverage from 25% to 87.5% and NLPD from 8.34 to 3.92.
- Risk-neutral density testbedThe repository applies the same machinery to option-implied risk-neutral densities. Market data is not published.
How the thinking developed
Why a measure, not two numbers
Wind and solar output is high exactly when prices fall. Separate point forecasts of price and production discard that negative covariance, which is what drives the cannibalisation effect.
Why a kernel on measures
Once the forecast is a joint distribution, similarity between forecasts has to be a distance between distributions. Wasserstein and Sinkhorn kernels provide it.
Reading a coverage number
A 25% empirical coverage at a nominal level is a bug signal rather than a modelling result. It led directly to the missing noise term.
Pipeline
- Option quotesRaw quotes for the underlying.
- Forward and rate estimationImplied forward and discount rate.
- Black-76 implied volatilityQuote-level implied volatilities.
- Total-variance interpolation30-calendar-day smile.
- SVI smile fitParametric fit of the smile.
- Arbitrage-constrained smoothingCall-price projection.
- Breeden–LitzenbergerDensity extraction.
- Quantile representationForward-normalised quantile functions.
- Forecast and evaluateWasserstein-kernel GP against persistence, a moment-based linear model, Wasserstein autoregression and an RBF GP, scored by held-out W₂ error.
The repository’s pipeline is for risk-neutral densities. Data-backed outputs are kept local under the data provider’s terms.