Accounting for executive stock options: a financial technology perspective

Abstract The Hull-White binomial approach to pricing Executive Stock Options (ESOs) offers a practical framework that accounts for important features like vesting, early exercise, and forfeiture-elements not captured by traditional Black–Scholes methods. However, a known weakness of the Hull-White approach is its slow convergence, which can limit its usability in applied settings. This paper introduces enhanced versions of the Hull-White model, drawing on improvements proposed by Boyle-Lau and Tian, to speed up convergence when barrier-like features are present. These refinements, referred to as Hull-White-Boyle-Lau and Hull-White-Tian enable faster, more accurate valuations that are easier to audit and reproduce. In addition to improving computational performance, we move beyond the standard fixed-rule approach by allowing early exercise to be endogenously determined. In high-dividend regimes, where early exercise becomes economically rational, the HWBL and HWTian models can efficiently capture the optimal early exercise point. This may assist practitioners when rationalizing to peers the selection of parameter inputs. The enhanced models align well with current accounting standards in the US, Europe, and China, and can support auditors and other professionals working within evolving regulatory frameworks globally.