Interest Rate Modelling (Finance and Capital Markets Series)

2017-07-07 02:10:07

Using Lagrange interpolation, fit a quadratic polynomial p ( x ), to node points x _{j ˆ’ 1} , x _j ,x _{j +1} . This takes the form

hence

and so evaluating this derivative at node x _j we have:

Hence we fine the polynomial S _j , j = 0, 1, , n ˆ’ 2 such that:

This gives rise to coefficient values defined by (see [ 20 ]):

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