In fitting the historical volatility structure of the HJM-factors, quadratic splines were used. Suppose there are N observations ?(t, ?_n), for n = 1, . . . , N. Show that all spline coefficients can be computed, if the data points are matched exactly, the condition

holds, and the first spline is only a linear function.

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o,(Tn+1) =0n+|(Tn+1) n+1 Int