|Code Listing by Fernando Nieuwveldt|
I originally posted this code in Recipe 577132 and this is a repost of that recipe with corrections since there was an error in the original recipe. Added here is an error analysis to show the effectiveness of the Laplace inversion method for pricing European options. One can test the accuracy of this method to the finite difference schemes. The laplace transform of Black-Scholes PDE was taken and the result was inverted using the Talbot...
I present a method of computing the 1F1(a,b,x) function using a contour integral. The method is based on a numerical inversion, basically the Laplace inversion. Integral is 1F1(a,b,x) = Gamma(b)/2\pi i \int_\rho exp(zx)z^(-b)(1+x/z)^(-a)dz, \rho...
This is a fast and highly accurate numerical method for the inversion of the Laplace transform
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