Limiting Cases of the Black-Scholes Type Asymptotics of Call Option Pricing in the Generalised CRR Model

Abstract

The article concerns the generalised Cox‑Ross‑Rubinstein (CRR) option pricing model with new formulas for changes in upper and lower stock prices. The formula for option pricing in this model, which is the Black‑Scholes type formula, and its asymptotics are presented. The aim of the paper is to analyse limiting cases of the obtained asymptotics using probability theory and later data from the Warsaw Stock Exchange. Empirical analyses of option pricing in the generalised CRR model confirm the calculated limits.