Continuous-time trading and emergence of volatility

Abstract

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.

7 pages; v2: new title and minor corrections

References in corpus (4)

• A new formulation of asset trading games in continuous time with essential forcing of variation exponent
• Game-theoretic versions of strong law of large numbers for unbounded variables
• Continuous-time trading and emergence of randomness
• Implications of contrarian and one-sided strategies for the fair-coin game