Kybernetika 34 no. 6, 713-724, 1998

Nonexpansive maps and option pricing theory

Vassili N. Kolokoltsov


The famous Black-Sholes (BS) and Cox-Ross-Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a deterministic approach to the option pricing that leads to a different type of generalisations of BS and CRR formulas characterised by more rough assumptions on common stocks evolution (which are therefore easier to verify). On the other hand, this approach is more elementary, because it uses neither martingales nor stochastic equations.