TY  - JOUR
ID  - Attalienti2020
LB  - Attalienti2020
AU  - Attalienti, Antonio
AU  - Bufalo, Michele
TI  - Option pricing formulas under a change of numèraire
ST  - Option pricing formulas under a change of numèraire
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 4
SP  - 451
EP  - 473
DO  - https://doi.org/10.7494/OpMath.2020.40.4.451
UR  - https://doi.org/10.7494/OpMath.2020.40.4.451
AB  - 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.
KW  - Black-Scholes formula
KW  - binomial model
KW  - martingale measures
KW  - numèraire
SN  - 1232-9274
ER  -