Bernstein's inequalities and their extensions for getting the Black-Scholes option pricing formula (Q273845)
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scientific article; zbMATH DE number 6572385
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bernstein's inequalities and their extensions for getting the Black-Scholes option pricing formula |
scientific article; zbMATH DE number 6572385 |
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Bernstein's inequalities and their extensions for getting the Black-Scholes option pricing formula (English)
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22 April 2016
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Bernstein's inequalities
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option pricing
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binomial model
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Cox-Ross-Rubinstein formula
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Black-Scholes formula
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rate of convergence
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The authors show an alternative derivation of the Black-Scholes formula for a European call option from the Cox-Ross-Rubinstein binomial formula by means of \textit{S. N. Bernstein}'s inequalities [Izv. Akad. Nauk SSSR, Ser. Mat. 7, 3--16 (1943; Zbl 0063.00339)] as well as \textit{A. M. Zubkov} and \textit{A. A. Serov}'s inequalities [Theory Probab. Appl. 57, No. 3, 539--544 (2013; Zbl 1280.60016); translation from Teor. Veroyatn. Primen. 57, No. 3, 597--602 (2012)].NEWLINENEWLINETheir results allow for a convergence rate \(1/\sqrt{n}\).
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