Efficient quadrature and node positioning for exotic option valuation

We combine the best features of two highly successful quadrature option pricing streams, improving the linked issues of numerical precision and abscissa positioning. Coupling the recombining abscissa (node) approach used in Andricopoulos, A., Widdicks, M., Duck, P., and Newton, D.P. (2003) (AWDN as well as AWND, 2007) with the Gauss-Legendre Quadrature (GQ) method of Sullivan, M.A. (2000) yields highly accurate and efficient option prices for a range of standard and exotic specifications including barrier options and in particular for NGARCH, CEV, and jump-diffusion processes. The improvements are due to manner in which GQ positions nodes and the use of these values without interpolation.