American Option Pricing: Optimal Lattice Models and Multidimensional Efficiency Tests

Abstract

This paper introduces a set of lattice techniques with a view to accelerating computation time and improving the accuracy of American Option valuation. Estimation speed can be enhanced through developing a parsimonious early exercise boundary search routine combined with reliance on dynamic memory and lattice truncation. Furthermore, Black-Scholes and Richardson extrapolation modifications to the lattices can also be applied individually and/or together to improve the accuracy of lattices. In this paper, we investigate the improvement introduced by obtaining the best combination of varying features. By introducing these techniques to the Leisen-Reimer and Tian binomial model, we can achieve a level of accuracy and efficiency combined that surpass analytical analogues prominent in the literature. Significantly, the Leisen-Reimer and Tian structure can accommodate arbitrary improvements in accuracy by simply increasing the density of their own mesh. Analytical methods generally do not afford much scope for optimising speed and efficiency in a granular fashion. We also compare efficient lattice models with analytical formulae for pricing different groups of options according to the deepness of American quality and the moneyness of the options. The appropriate model is recommended for pricing particular types of the options. Lattices importantly afford an explicit trade-off locus between accuracy and speed that can be navigated according to predetermined precision tolerance levels and option types. This should have practical relevance to trading platforms that require real-time estimates of implied volatility.