English

Discrete dividends after maturity adjust the stock and strike prices

Mathematical Finance 2026-07-27 v1

Abstract

The standard method to price European calls on a discrete dividend-paying stock is to subtract the present value of the dividends from the initial stock price in the Black-Scholes formula. However, when there are dividends after maturity, this is inconsistent with the model. Within the escrowed dividend model, we highlight an extension of the Black-Scholes formula in which those dividends after maturity adjust both the stock price and strike price, allowing for calls over all maturities to be priced in a model-consistent way. As a related application to American calls with a single dividend before maturity, we establish a neglected case where it is always optimal to early exercise and derive an extension of the Roll-Geske-Whaley formula when there are dividends after maturity, including fully characterising the optimal exercise policy.

Keywords

Cite

@article{arxiv.2607.24973,
  title  = {Discrete dividends after maturity adjust the stock and strike prices},
  author = {Kevin W. Lu},
  journal= {arXiv preprint arXiv:2607.24973},
  year   = {2026}
}