Quadratic variation of financial asset prices

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Financial asset prices vary not only in level and trajectory but also in magnitude and type of variability during trading periods. Accurate quantification of price variability is essential for risk and valuation applications, necessitating concepts that truly reflect variability exposure. This involves considering factors such as the amount of available data, alignment of data assumptions with empirical realities, and the time horizon and purpose of the variation measure (modeling, forecasting, validation). The review focuses on existing univariate variance concepts based on the quadratic variation of continuous-time price processes, assessing their empirical applicability, particularly for electricity forward contracts traded on the Nord Pool Energy Exchange. Key questions addressed include the sensitivity of methods to decompose realized variance into continuous and jump components concerning flat prices and lack of trading, strategies to enhance robustness given finite sample issues, and evaluating the plausibility of detected jump components. The findings indicate that existing decomposition methods are sensitive to flat prices and no trading. Consequently, several robustification approaches are proposed, along with plausibility checks for jump components in empirical contexts. The robustified methods are applied to analyze electricity forward contracts, linking changes in continuous variation and jump components to tradin