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In June of 2001, Tokyo Electric Power Company (TEPCO) and Tokyo Gas Supply Company (TGSC) made a zero‐cost risk swap contract on the average temperature of August and September of 2001 in Tokyo for their adverse situations. This is an exchange of two options on the average temperature, by which TEPCO and TGSC can, respectively, hedge against a cold summer and a hot summer. The purpose of this paper is to develop a theoretical framework to evaluate the fairness or rationality of such a zero‐cost weather risk swap, derive some conditions to check the rationality and empirically evaluate the fairness of the above temperature risk swap between the two companies.

To provide a framework for analyzing weather risk swap, the authors used a statistical approach and a basic analysis is given with data and simulation.

First, the authors define the concept of full equivalence and moment equivalence of two options on a weather index and then derive some conditions for full and moment equivalences. Third, using the stochastic volatility model in Kariya et al., it is shown that the options in the TEPCO–TGSC risk swap are neither fully equivalent nor moment‐equivalent as they stand.

This paper originates the weather risk swap valuation problem and gives a framework to analyze and value the equivalence of a temperature risk swap. This method can be applied to various possible risk swaps for risk management.