Opuscula Mathematica
Opuscula Math. 40, no. 4 (2020), 451-473

Option pricing formulas under a change of numèraire

Antonio Attalienti
Michele Bufalo
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.
Mathematics Subject Classification: 91B25, 60G46.
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About the authors ▼
Antonio Attalienti (corresponding author)
https://orcid.org/0000-0003-4443-9763
Università degli Studi di Bari Aldo Moro, Department of Business and Law Studies, Bari, I-70124 Italy
Michele Bufalo
https://orcid.org/0000-0002-1161-8872
Università degli Studi di Roma "La Sapienza", Department of Economics and Finance, Roma, I-00185 Italy
About the article ▼
Communicated by Massimiliano Ferrara.
Received: 2020-02-07.
Accepted: 2020-05-09.
Published online: 2020-07-09.
Cite this article as ▼
Antonio Attalienti, Michele Bufalo, Option pricing formulas under a change of numèraire, Opuscula Math. 40, no. 4 (2020), 451-473, https://doi.org/10.7494/OpMath.2020.40.4.451.
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