Option pricing formulas under a change of numeraire

• Autorzy: Attalienti Antonio , Bufalo Michele

Identyfikatory

DOI

10.7494/OpMath.2020.40.4.451

• Języki publikacji: EN

Abstrakty

EN

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 numeraire 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.

Słowa kluczowe

EN

Black-Scholes formula; binomial model; martingale measures; numeraire

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 4
• Strony: 451--473
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Attalienti Antonio

• Universita degli Studi di Bari Aldo Moro Department of Business and Law Studies Bari, 1-70124 Italy

autor

Bufalo Michele

• Universita degli Studi di Roma "La Sapienza" Department of Economics and Finance Roma, 1-00185 Italy

Bibliografia

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• [7] M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer-Verlag Berlin Heidelberg, 2005.
• [8] L.T. Nielsen, Understanding N(di) and N(d,2): Risk-adjusted probabilities in the Black-Scholes model, Revue Finance 14 (1993), 95-106.
• [9] L.T. Nielsen, Pricing and Hedging of Derivative Securities, Oxford University Press, 1999.
• [10] S. Shreve, Stochastic Calculus for Finance I: the Binomial Asset Pricing Model, Springer-Verlag New York, 2004.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).