The Kriging weights w_i1,w_i2,w_i3,…w_ik can be used to estimate the fair value of VA contracts x ⃑_i by the following formula,
y ̂_i=∑_(j=1)^k▒〖w_ij∙y_j 〗.
The kriging weights can be calculated by the following linear equations,
Where the is a control variable, which is used to make sure that ∑_(j=1)^k▒w_ij =1.
V_rs=α+exp(-3/β D(z ⃑_r,z ⃑_s,λ)),r,s=1,2,3,…,k,
D_ij=α+exp(-3/β D(x ⃑_i,z ⃑_j,λ)),j=1,2,3,…,k,
The D(.) function is the distance function mentioned in the clustering section,α≥0 and β≥0 are two parameters. The above linear equation system has a unique solution because D(z ⃑_r,z ⃑_s,λ)>0 for all r,s=1,2,3,…,k,.
Then the fair value of whole portfolio X=(x ⃑_1,x ⃑_2,x ⃑_3,…,x ⃑_n)can be estimated by the following formula,…