Page 228 - Contributed Paper Session (CPS) - Volume 3

CPS2002 Atina A. et al.
to use. One of the association measurements which can measure dependency
structure both linear and non-linear is rank correlation consists of Kendall’s
Spearman’s . The two measurements can be expressed as a multivariate
distribution function called copula. Copula function has been widely used to
identify dependency structures between two variables, including in agriculture
sector. Zhu et al. (2008) modelled the dependency structure between corn and
soybean yield and price using copula. Xu et al. (2010) measured the spatial
dependency of the weather risk in some areas and modelled its impact to the
indemnity payment of crop insurance using copula. Xu et al. (2010) modelled
the joint loss distribution based on the systemic weather risk using hierarchical
copula.
In this study, we aim to identify the dependency structure between
weather risk, in this case is temperature change, and the agricultural yield
using copula models. The best copula model is selected to build a simulation
to estimate yield-based agricultural losses. Furthermore, we estimate the value
at risk of the agricultural losses by using the distribution of the estimated
yield-based agricultural losses obtained from the copula modelling.

2. Model Framework

2.1 Copula Modelling
Following Xu et al. (2010), the dependency structure between weather risk
and agricultural yield can be modelled using copula function. Suppose that
F X ,Y (x , ) y is a joint distribution function with marginal distribution functions

F X (x ) and F Y ( ) y . There is a copula C such that (Nelsen, 2006)

F X ,Y (x , y ) C= (F X (x ), F Y (y )) (1)

If F X (x ) and F Y ( ) y continue, then C is unique. Otherwise, if C is copula,
F X (x ) and F Y ( ) y are distribution functions, then F X ,Y (x , ) y is a joint
distribution function with marginal distribution function F X (x ) and F Y ( ) y .
Eq. (1) can also be written as

) C
F X ,Y (x , y = (u , ) v (2)
where u = F X (x ) and v = F Y ( ) y which are uniformly distributed at ,0[ ]. 1
Eq. (1) gives information about marginal distribution and copula function.
In copula concept, X and Y can be modelled with any distribution function.
Therefore, before selecting the best copula function, distribution fitting for
both marginal variables has to be done first.

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