Open AccessProximity of Bachelier and Samuelson Models for Different Metrics
Author(s) -
С. Н. Смирнов,
Dmitry Sotnikov
Publication year - 2021
Publication title -
review of business and economics studies
Language(s) - English
Resource type - Journals
eISSN - 2311-0279
pISSN - 2308-944X
DOI - 10.26794/2308-944x-2021-9-3-52-76
Subject(s) - metric (unit) , lipschitz continuity , computation , probabilistic logic , mathematics , volatility (finance) , bounded function , nonlinear system , econometrics , mathematical economics , mathematical optimization , economics , statistics , mathematical analysis , algorithm , operations management , physics , quantum mechanics
This paper proposes a method of comparing the prices of European options, based on the use of probabilistic metrics, with respect to two models of price dynamics: Bachelier and Samuelson. In contrast to other studies on the subject, we consider two classes of options: European options with a Lipschitz continuous payout function and European options with a bounded payout function. For these classes, the following suitable probability metrics are chosen: the Fortet-Maurier metric, the total variation metric, and the Kolmogorov metric. It is proved that their computation can be reduced to computation of the Lambert in case of the Fortet-Mourier metric, and to the solution of a nonlinear equation in other cases. A statistical estimation of the model parameters in the modern oil market gives the order of magnitude of the error, including the magnitude of sensitivity of the option price, to the change in the volatility.