@Article{Attalienti2020,
author = "Attalienti, Antonio and Bufalo, Michele",
title = "Option pricing formulas under a change of numèraire",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "4",
pages = "451--473",
doi = "https://doi.org/10.7494/OpMath.2020.40.4.451",
url = "https://doi.org/10.7494/OpMath.2020.40.4.451",
abstract = "We present some formulations of the Cox-Ross-Rubinstein and Black-Scholes formulas for European options obtained through a suitable change of measure, which corresponds to a change of numèraire for the underlying price process. Among other consequences, a closed formula for the price of an European call option at each node of the multi-period binomial tree is achieved, too. Some of the results contained herein, though comparable with analogous ones appearing elsewhere in the financial literature, provide however a supplementary widening and deepening in view of useful applications in the more challenging framework of incomplete markets. This last issue, having the present paper as a preparatory material, will be treated extensively in a forthcoming paper.",
keywords = "Black-Scholes formula, binomial model, martingale measures, numèraire",
issn = "1232-9274"
}