Integrating Feynman Kac Equations Using Hermite Quintic Finite Elements
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Overview: The Feynman‐Kac solver introduced in the newest release of the IMSL® C Numerical Library has been tailored for the quantitative analyst involved in developing financial modeling applications, including Black‐Scholes with European type or American type exercise opportunities on Calls or Puts. Methods are given for numerically solving a generalized version of the Feynman‐Kac partial differential equation. The solution is represented as a linear combination of piece‐wise Hermite quintic polynomials, a choice which enables efficient and extremely accurate computation of “The Greeks”. The time‐dependent solution coefficients are computed by finite element Galerkin procedures. The twice‐differentiable representation has the attributes of being a high‐order method that allows easier evaluation of the solution and certain of its partial derivatives. Boundary values and initial conditions are required.