In this paper we present a spectral method based on the improved Lagrange formula to compute European, digital, and butterfly spread options.
With slight modifications, the Lagrange formula is indeed of great practical use.
A modified Lagrange formula. Following , the Lagrange formula (3.1) can be rewritten in such a way that [p.sub.N](x) is computed in O(N) operations.
Of course, it is generally not possible to change the order of the signs lim and [SIGMA] to end in the classic (Waring) Lagrange formula
. The proof is given in the Appendix, and (8) is true for the class of functions with Fourier transform which vanishes outside [-[pi], [pi]] and for stationary random processes with power spectrum fulfilling the same condition.