Weather Swap Pricing and the Optimal Size for Medium-Range Forecast Ensembles

Stephen Jewson Risk Management Solutions, London, United Kingdom

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Christine Ziehmann Risk Management Solutions, London, United Kingdom

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Abstract

Weather swap pricing involves predicting the mean temperature for the current month with the highest possible accuracy. The more days of skillful forecasts that are available, the better the monthly mean can be predicted. The ensemble mean of a downscaled medium-range dynamical forecast ensemble such as the ECMWF or Medium-Range Forecast (MRF) ensembles can be used, with historical data, to make this prediction. Assuming finite computing resources, there must exist an optimum balance between the length of the forecast and the size of the ensemble for which this prediction will be the most accurate. An idealized model is used to show that, for this purpose, the ECMWF ensembles are too large and the forecasts are too short. The MRF ensembles are much closer to the optimum design but could still possibly benefit from increasing the length of the forecast slightly, at the expense of the size of the ensemble.

Corresponding author address: Stephen Jewson, RMS, 10 Eastcheap, London EC3M 1AJ, United Kingdom. Email: x@stephenjewson.com

Abstract

Weather swap pricing involves predicting the mean temperature for the current month with the highest possible accuracy. The more days of skillful forecasts that are available, the better the monthly mean can be predicted. The ensemble mean of a downscaled medium-range dynamical forecast ensemble such as the ECMWF or Medium-Range Forecast (MRF) ensembles can be used, with historical data, to make this prediction. Assuming finite computing resources, there must exist an optimum balance between the length of the forecast and the size of the ensemble for which this prediction will be the most accurate. An idealized model is used to show that, for this purpose, the ECMWF ensembles are too large and the forecasts are too short. The MRF ensembles are much closer to the optimum design but could still possibly benefit from increasing the length of the forecast slightly, at the expense of the size of the ensemble.

Corresponding author address: Stephen Jewson, RMS, 10 Eastcheap, London EC3M 1AJ, United Kingdom. Email: x@stephenjewson.com

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