Spatial Aggregation and Weather Risk Management

(7)                    Y^det = Y —, t = 1971,...,2002

t t          t_r

Y_t
where Y_t are observed yields and Y_t^trare the corresponding yield trends.

The negative effect of temperature stress on corn yields during the summer season
is well accepted (see, e.g., Monjardino, Smith and Jones 2005; Dixon et al 1994; Tiegen
1991; and Kaufmann and Snell 1997). Furthermore, temperature derivatives are likely
the most feasible weather variable on which to structure weather contracts from a
transaction cost standpoint. Thus temperature derivatives are adopted for this study. The
temperature variables used are Accumulated Cooling Degree Days (ACDD’s) for the
summer season: June, July, and August. Agronomic experiments indicate that cooling
degree days (CDD’s) are more relevant to crop yields than outright temperature
measurements (Schlenker, Hanemann and Fisher 2006). Further, the temperature
derivatives traded on the CME are written on ACDD indexes. The number of CDD’s for
a single day is defined as the amount by which the average temperature is above the
reference temperature, sixty-five degrees Fahrenheit. Explicitly, the number of CDD’s
on any day t is given by
(8)                        CDD_t = Max(0,T_t - 65)

where T_t is the average temperature on day t. The average temperature is the simple
arithmetic average of the daily maximum and minimum temperatures. The index of
ACDD’s on any date, t, is simply defined as

M

(9)                 ACDD_t^M,N = ∑CDD_t, t=M -N,...,M

t=M -N

where M - N is the first day of the contract period and M is the expiration date.

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