Continuous-time trading and emergence of volatility

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Vovk, Vladimir
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Abstract
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This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.
Comment: 7 pages; v2: new title and minor corrections
Keywords
Quantitative Finance - Trading and Market Microstructure, Mathematics - Probability, 60G17, 60G05, 60G44
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