The hexanomial lattice for pricing multi-asset options
Abstract 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 ρ ij 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 ( Δ t ) ⩽ ρ ij ⩽ 1 - O ( Δ t ) for all pairs of assets i and j , where Δ t 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.
With Shanghai stock exchange market as a research object, this paper studies the complexity of the stock exchange market using the cellular automata theory and model. With the fractal theory as a tool, the R/S method is used to compare the real and the simulated data, which verifies the validity of the simulation. In the CA model, with different initial values and rules, we can improve the study on complexity in the stork exchange market.