Theoretical and Empirical Essays on the Dynamics of Financial and Energy Markets

This thesis is inspired by two main lines of research. Topics are analyzed in Chapters 1, 3, 4, 5 and 6. Chapter 2 is devoted to help the reader unfamiliar with the concepts of measure theory and stochastic processes. The first line of research is dedicated to highlight a drawback of the standard economic equilibrium model. We start from a question mainly raised by the ecological problem: is the economic equilibrium consistent with the physical world? The answer seems to be negative. Economic equilibrium theory estab- lishes the optimal level of production and consumption of goods. Consumption is, in fact, a social issue. It depends on what consumers prefer for their own utility. For this reason consumption is not directly related to the laws of physics. However production is unavoidably linked with a physical process: the ther- modynamic transformation of basic commodities in elaborated one, useful for consumption. Despite this fact most part of economic models, in the mainstream literature, completely neglect the thermodynamic cycles hidden in every production process. In the last two decades the ecological problem has gained attention over the scientific community, focusing on the role of thermodynamic efficiency in the conversion of energy into work as a factor of economic growth. In Chapter 1 we propose an analitycal approach to economic equilibrium which takes into account for thermodynamic efficiency. Our idea is tho show that if irreversibility is present the classical economic equilibrium is changed, resulting in a more parsimonious use of energy. Standard economic equilibrium implies that the equilibrium itself remains unchanged if the numeraire adopted to price good is changed, i.e. all numeraires are equivalent. This is a strong and quite controversial result: it is intuitive that, being the conversion of energy into work intrinsically irreversible, energy is a special commodity and it is not equivalent to the other ones. Pricing in terms of energy should not be equivalent to pricing in terms of other goods, which in fact are obtained by energy itself. Moreover the proposed ”thermodynamic-consistent” economy turns back into the classical one if the production process is reversible. In this sense economic theory implicitly assumes that all production processes are reversible. This assumption conflicts with any real world production process. The second line of research is independent from the first one and it is mainly devoted to the analysis of discontinuities of assets quoted in financial markets. Several drastic events are known to have influenced and changed the status of the financial markets. In such a situation the uncertainty hidden in financial assets increased rapidly getting the markets into a very turbulent state. Examples of such events are the 1929 crash of Wall Street, Black Monday crisis of 1987 and the 9/11 terrorist attack. In fact these are 1 2 rare events of very high intensity. Many discontinuities of smaller amplitude affect the behavior of assets: on the average we can identify, visually, 5−10 of such abrupt variations per year. Such kind of rapid and intense variations are usually referred as jumps. In this context we expect that, after a jump has occurred, the market switches in a new status characterized by an high level of volatility. As a consequence jumps are expected to have a predictive power on the future behaviour of assets. Despite this is a very intuitive fact it has not yet proved in the financial literature. A volatility forecasting model requires the definition of a volatility proxy. The idea is that proxies adopted in the literature for forecasting purposes are, in fact, contaminated by the presence of jumps in finite sample. In this context the forecasting power of jumps on future volatility cannot be revealed. In order to highlight such a feature it is needed a precise estimate of the jump component. In this spirit we propose in Chapter 3 a powerful jump separation technique and we test its performances on eight markets of electricity. The separation technique we adopt is taken from very recents results of the financial literature and only requires the introduction of a threshold. In Chapter 4 we construct precise volatility estimators using the threshold separation technique. This approach allows for a volatility estimation unaffected by jumps. Moreover in Chapter 5 we show that a jump purified estimate of volatility allow for a better investigation of its memory properties. Finally in Chapter 6 we construct a volatility forecasting model based on the proposed estimators. Being based on an accurate separation of continuous and discontinuous component of volatility, the model reveals the forecasting power of jumps on future volatility. Moreover we find that the forecasting power of jumps extend to at least one month. A dazzling example of the turbulence triggered by discontinuous variations is the recent crisis of markets. In September 2008 a global big crash has occurred in most part of stock exchanges. Since ever markets show an high level of volatility, characterized by large returns of both negative and postivie intensity. In this sense our results are very topical and constitute a basis for further investigations.