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Nonexpansive maps and option pricing theory
Kybernetika, Tome 34 (1998) no. 6, pp. 713-724 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 91B24, 91B28, 91B42, 91G20
Keywords: option pricing; stocks pricing evolution; Black-Scholes formula 
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Kolokoltsov, Vassili N. Nonexpansive maps and option pricing theory. Kybernetika, Tome 34 (1998) no. 6, pp. 713-724. http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a8/

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