We provide a valuation formula for emission allowance. Assuming that the value of emission allowance on the last day of a trading phase is equal to a spread of commodity prices (e.g. electricity and natural gas) when the spread is positive and less than the penalty, we show that the emission...

Despite the worldwide popularity of CDD- and HDD-type weather derivatives based on temperature, a different class of weather derivatives, so-called summer day options, is more popular in Japan; the payoffs are determined by the number of summer days (i.e., the days whose average temperature is...