Abstract
We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.
Highlights
This paper deals with the valuation of American-style basket options
For European- and Bermudan-style basket options, leading to high-dimensional partial differential equations (PDEs), an effective approach has been introduced by Reisinger and Wittum [1] and studied in, e.g., Reisinger and Wissmann [2,3,4] and In ’t Hout and Snoeijer [5]
This approach is based on a principal component analysis (PCA) and yields an approximation formula for the value of the basket option that requires the solution of a limited number of only low-dimensional PDEs
Summary
This paper deals with the valuation of American-style basket options. Basket options constitute a popular type of financial derivatives and possess a payoff depending on a weighted average of different assets. An American-style basket option is a financial contract that gives the holder the right to buy or sell a prescribed weighted average of d assets for a prescribed strike price K at any given single time up to and including a prescribed maturity time T. PDCPs. In Section 3.1, an efficient discretisation of the one- and two-dimensional PDEs for European basket options is described, which employs finite differences on a nonuniform spatial grid followed by the Brian and Douglas Alternating Direction Implicit (ADI) scheme on a uniform temporal grid.
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