The hexanomial lattice for pricing multi-asset options

摘要

Multi-asset options are important financial derivatives. Because closed-form solutions do not exist for most of them, numerical alternatives such as lattice are mandatory. But lattices that require the correlation between assets to be confined to a narrow range will have limited uses. Let ρij denote the correlation between assets i and j. This paper defines a (correlation) optimal lattice as one that guarantees validity as long as -1+O(Δt)⩽ρij⩽1-O(Δt) for all pairs of assets i and j, where Δt is the duration of a time period. This paper then proposes the first optimal bivariate lattice (generalizable to higher dimensions), called the hexanomial lattice. This lattice furthermore has the flexibility to handle a barrier on each asset. Experiments confirm its excellent numerical performance compared with alternative lattices.