### What is the payoff from a call option on the cumulative

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Weather derivatives are often written in terms of HDD and CDD, heating degree days and cooling degree days, where on a given day, HDD = max(0,65-A) CDD = max(0,A-65) A = average of the day’s low and high temperatures. The cumulative HDD and cumulative CDD over a span of time is just the sum of HDDs or CDDs. Heating degree days are a measure of the amount you have to heat in order to keep a temperature of 65 and cooling degree days are a measure of the amount you have to cool in order to keep an average temperature of 65. Suppose that each day in July (1st – 31st ) the minimum temperature is 68 and the maximum is 82. What is the payoff from a call option on the cumulative CDD during July with a strike of 250 and a payment of \$5,000 per degree day?

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