Frowin C. SchulzQuadratic Variation of Financial Asset Prices

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Financial asset prices differ not only in their level and trajectory, but also in their magnitude and type of variability within trading periods. As financial agents require quantifying the price variability of a financial asset over a certain period of time in many risk- and valuation-related applications, it is crucial to reflect appropriate concepts which provide an accurate picture of the variability exposure. The scientific elaboration of an adequate concept in light of the practical necessities demands the consideration of all issues related to the quantification of price variability. These include available data amount, concurrence of the assumptions about the data generating process with the empirical actuality, time horizon and purpose of the variation measure (modeling, forecasting or validation). Having the scope of scientific and practical attributes in mind, we review existing univariate variance concepts, which are based on the quadratic variation of continuous-time price processes. Furthermore, we discuss their empirical convenience and apply the concept to a specific class of financial assets. These are electricity forward contracts traded on the Nord Pool Energy Exchange.

In particular, the object of research in this thesis is:

• I. How sensitive are existing methods to decompose realized variance in its continuous and jump component with respect to flat prices and no trading?
• II. How can we robustify these methods given the finite sample issues of flat prices and no trading?
• III. How can we argue in empirical applications whether a detected jump component is plausible?
• IV. How can we explain periods of high and low continuous variation and the occurrence and size of a jump component for electricity forward contracts traded on the Nord Pool Energy Exchange?

In this thesis we find that existing methods to decompose realized variance in its continuous and jump component are quite sensitive to flat prices and no trading. For that reason, we propose several approaches to robustify existing methods with respect to flat prices and no trading and we discuss plausibility checks for detected jump components in empirical applications. Finally, we utilize the robustified approaches to a range of electricity forward contracts traded on the Nord Pool Energy Exchange to form the basis for explaining changes in continuous variation and the occurrence and size of a jump component. Changes in the corresponding components are explained with trading activity and certain news announcements, here urgent market messages.

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