Abstract
We give an overview of our work since 2000 on an alternate theory of Option pricing and contingent claim hedging based upon the so-called “interval model” of security prices, which let us develop a consistent theory in discrete and continuous trading within the same model, taking transaction costs into account from the Start. The interval model rules out crises on the stock market. While Samuelson's model does not, so does in practice Black and Scholes' theory in its assumption of instantaneous, continuous trading. Our theory does not make use of any probabilistic knowledge (or rather assumption) on market prices. But we show that Black and Scholes theory does not either.
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Bernhard, P. (2005). The Robust Control Approach to Option Pricing and Interval Models: An Overview. In: Breton, M., Ben-Ameur, H. (eds) Numerical Methods in Finance. Springer, Boston, MA. https://doi.org/10.1007/0-387-25118-9_4
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DOI: https://doi.org/10.1007/0-387-25118-9_4
Publisher Name: Springer, Boston, MA
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