Gapeev, P. V. Calculation of the high and low prices of European-type options. (English. Russian original) Zbl 0921.90017 Russ. Math. Surv. 52, No. 4, 828-829 (1997); translation from Usp. Mat. Nauk 52, No. 4, 199-200 (1997). Summary: A. N. Shiryaev, Yu. M. Kabanov, O. D. Kramkov and A. V. Mel’nikov [Theory Probab. Appl. 39, No. 1, 14-60 (1994; Zbl 0833.60064)] considered recently the Cox-Ross-Rubinstein model, with the \((B,S)\)-market assumed to be complete. A definition is given for rational pricing of a European-type option. We consider the question of how to define the concept of the buying price and selling price of an option in a scheme in which an active trader can not only sell but also buy European-type options, with hedging of both. A model of a non-complete market is treated in which the set of martingale measures consists of more than one measure. MSC: 91G20 Derivative securities (option pricing, hedging, etc.) Keywords:Cox-Ross-Rubinstein model; European-type option; hedging; non-complete market; martingale measures Citations:Zbl 0833.60064 PDFBibTeX XMLCite \textit{P. V. Gapeev}, Russ. Math. Surv. 52, No. 4, 828--829 (1997; Zbl 0921.90017); translation from Usp. Mat. Nauk 52, No. 4, 199--200 (1997) Full Text: DOI