Extending quadrature methods to value multi-asset and complex path dependent options

By Ari D. Andricopoulos, Martin Widdicks, David P. Newton, Peter W. Duck. Journal of Financial Economics, 2007

61 citations recorded by the source corpus.

Abstract The exposition of the quadrature (QUAD) method (Andricopoulos, Widdicks, Duck, and Newton, 2003. Universal option valuation using quadrature methods. Journal of Financial Economics 67, 447–471 (see also Corrigendum, Journal of Financial Economics 73, 603 (2004)) is significantly extended to cover notably more complex and difficult problems in option valuations involving one or more underlyings. Trials comparing several techniques in the literature, adapted from standard lattice, grid and Monte Carlo methods to tackle particular types of problem, show that QUAD offers far greater flexibility, superior convergence, and hence, increased accuracy and considerably reduced computational times. The speed advantage of QUAD means that, even under the curse of dimensionality, it is not necessary to resort to Monte Carlo methods (certainly for options involving up to five underlying assets). Given the universality and flexibility of the method, it should be the method of choice for pricing options involving multiple underlying assets, in the presence of many features, such as early exercise or path dependency.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/6ebdc31f2af1773a08acda90bbdad10fe9741d92

Citations in the corpus

• Pricing early-exercise and discrete barrier options by fourier-cosine series expansions (2009, unknown): “Recently, transform methods have been generalized to solving somewhat more complicated option contracts, like Bermudan, American or barrier options, see, for example, [32, 21, 3, 4, 29, 41, 17, 40].”