On Modeling Questions In Security Valuation

Ernst Eberlein

Mathematical Finance, 1992, vol. 2, issue 1, 17-32

Abstract: After mentioning some deficiencies of the standard Black‐Scholes model for the valuation of call options, we discuss discrete models which allow price changes of the underlying security at discrete time points only. It is shown that, given any distribution with a moment higher than 2, the paths of the Black‐Scholes stock price process can be approximated uniformly as closely as one wishes by discrete paths generated by this distribution. Based on this approximation, discrete‐time trading strategies are defined. Convergence (in measure and almost surely) of the corresponding financial gain processes is obtained. the results show the robustness of the Black‐Scholes model.

Date: 1992
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https://doi.org/10.1111/j.1467-9965.1992.tb00023.x

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