Delphine Lautier

Systemic Risk in Energy Derivative Markets: A Graph-Theory Analysis

This article uses graph theory to provide novel evidence regarding market integration, a favorable condition for systemic risk to appear in. Relying on daily futures returns covering a 12-year period, we examine cross- and inter-market linkages, both within the commodity complex and between commodities and other financial assets. In such a high dimensional analysis, graph theory enables us to understand the dynamic behavior of our price system. We show that energy markets - as a whole - stand at the heart of this system. We also establish that crude oil is itself at the center of the energy complex. Further, we provide evidence that commodity markets have become more integrated over time.

Statistical Properties of Derivatives: A Journey in Term Structures

This article presents an empirical study of thirteen derivative markets for commodity and financial assets. This paper goes beyond statistical analysis by including the maturity as a variable for futures contracts’s daily returns, from 1998 to 2010 and for delivery dates up to 120 months. We observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the Samuelson effect. The comparison of the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the Levy stable region. Finally, we compute the average tail exponent for each maturity and we observe two regimes of extreme events for derivative markets, reminding of a phase diagram with a sharp transition at the 18th delivery month.

Simple and extended Kalman filters: an application to term structures of commodity prices

This article presents and compares two different Kalman filters. These methods provide a very interesting way to cope with the presence of non-observable variables, which is a frequent problem in finance. They are also very fast even in the presence of a large information volume. The first filter presented, which corresponds to the simplest version of a Kalman filter, can be used solely in the case of linear models. The second filter – the extended one – is a generalization of the first one, and it enables one to deal with non-linear models. However, it also introduces an approximation in the analysis, whose possible influence must be appreciated. The principles of the method and its advantages are first presented. It is then explained why it is interesting in the case of term structure models of commodity prices. Choosing a well-known term structure model, practical implementation problems are discussed and tested. Finally, in order to appreciate the impact of the approximation introduced for non-linear models, the two filters are compared.

Systemic risk and complex systems: a graph theory analysis

This chapter summarizes several empirical studies in finance, undertaken through the prism of the graph theory. In these studies, we built graphs in order to investigate integration and systemic risk in derivative markets. Several classes of underlying assets (i.e. energy products, metals, financial assets, agricultural products) are considered, on a twelve-year period. In such a high dimensional analysis, the graph theory enables us to understand the dynamic behavior of our price system. The dimension of the fully connected graph being high, we rely on a specific type of graphs: Minimum Spanning Trees (MSTs). Such a tree is especially interesting for the study of systemic risk: it can be assimilated into the shortest and most probable path for the propagation of a price shock. We first examine the topology of the MSTs. Then, given the time dependency of our correlation-based graphs, we study their evolution over time and their stability.

Hedging Pressure and Speculation in Commodity Markets

We propose a comprehensive equilibrium model to examine the interaction between the physical and the derivative markets of a commodity. The model comprises four types of traders: hedgers of future sales and hedgers of future purchases, both of which operate on all markets; speculators who operate only on the futures market; and spot traders. We provide the necessary and sufficient conditions on the fundamentals of this economy for a rational expectations equilibrium to exist, and we show that it is unique. The model exhibits a remarkable variety of behaviors at equilibrium that we can use to analyze price relations in any market according to the characteristics of the commodity under consideration. Further, through a comparative statics analysis, we are able to precisely identify the losers and winners in the financialization of the commodity markets. Therefore, this paper clarifies the political economy of regulatory issues like speculators’ influence on prices.

Information Flows across the Futures Term Structure: Evidence from Crude Oil Prices

We apply the concepts of mutual information and information flows and we built directed graphs to investigate empirically the propagation of price fluctuations across a futures term structure. We focus on price relationships for North American crude oil futures because this key market experienced several structural shocks between 2000 and 2014: financialization (starting in 2003), infrastructure limitations (in 2008-2011) and regulatory changes (in 2012-2014). Wefind large variations over time in the amount of information shared by contracts with different maturities. The mutual information increased substantially starting in 2004 but fell back sharply in 2012-2014. In the crude oil space, our findings point to a possible re-segmentation of the futures market by maturity in 2012-2014. This raises questions about the causes of market segmentation. In addition, although on average short-dated contracts (up to 6 months) emit more information than backdated ones, a dynamic analysis reveals that, after 2012, similar amounts of information flow backward as flow forward along the futures maturity curve. Moreover, the directions of the transfers between pairs of maturities become drastically different. This has implications for the Samuelson effect.Relying on conditional entropy and on the notion of information transfer, we investigate price relationships in the most important commodity futures market: the American crude oil market. We first show that the information shared by futures contracts with different delivery dates increases during the period under scrutiny (i.e. 2000-2011). This is especially true for intermediate maturities. When focusing on information transfer, on average on the whole period, it appears that short-term maturities emit more information than long-term ones. This is consistent with the normal functioning of a futures market. A dynamic analysis however reveals that the relative importance of information flows emerging in the far end of the curve (for long-term maturities) arises as integration progresses in the crude oil market. The transmission of shocks from the paper to the physical markets is thus facilitated. Last but not least, the direction of prices moves becomes less stable as time goes on. On the theoretical point of view, these findings raise questions about the segmentation theory and the Samuelson effect.

Volatility in electricity derivative markets: The Samuelson effect revisited

This article proposes an empirical study of the Samuelson effect in electricity markets. Our motivations are twofold. First, although the literature largely assesses the decreasing pattern in the volatilities along the price curve in commodity markets, it has not extensively tested the presence of such a dynamic feature in electricity prices. Second, the analysis of a non-storable commodity enriches the literature on the behavior of commodity prices. Indeed, it has been sometimes asserted that the Samuelson effect results from the presence of inventories. We examine the four most important electricity futures markets worldwide for the period from 2008 to 2014: the German, Nordic, Australian, and US markets. We also use the American crude oil market as a benchmark for a storable commodity negotiated on a mature futures market. Our analysis has two steps: i) in addition to the traditional tests, we propose and test a new empirical implication of the Samuelson effect: price shocks should spread from the physical market to the paper market, and not the reverse; ii) based on the concept of “indirect storability”, we investigate the link between the Samuelson effect and the storability of the commodity. We find evidence of a Samuelson effect in all of the electricity markets and show that storage is not a necessary condition for such an effect to appear. These results should be taken into account for the understanding of the dynamic behavior of commodity prices, for the valuation of electricity assets, and for hedging operations.

Dynamic Hedging Strategies: An Application to the Crude Oil Market

This article analyses long-term dynamic hedging strategies relying on term structure models of commodity prices and proposes a new way to calibrate the models which takes into account the error associated with the hedge ratios. Different strategies, with maturities up to seven years, are tested on the American crude oil futures market. The study considers three recent and efficient models respectively with one, two, and three factors. The continuity between the models makes it possible to compare their performances which are judged on the basis of the errors associated with a delta hedge. The strategies are also tested for their sensitivity to the maturities of the positions and to the frequency of the portfolio rollover. We found that our method gives the best of two seemingly incompatible worlds: the higher liquidity of short-term futures contracts for the hedge portfolios, together with markedly improved performances. Moreover, even if it is more complex, the three-factor model is by far, the best.

Energy Finance: The Case for Derivative Markets

For several years, the number of energy derivatives markets has been increasing at a tremendous rate. The same is true for the prices and the transactions volumes of energy futures contracts, with the noticeable exception of the recent crisis, in 2008–9. Such sustained growths naturally give rise to questions. What are the real dangers of such a development? Are derivatives markets always characterised by a high leverage effect, by opacity and liquidity problems? Do all these markets and transactions really respond to a need? Should the regulating authorities restrain further the transactions of speculators in such markets, before they introduce excess volatility, capable of destabilising the underlying physical markets? This chapter proposes answers to these questions, or at least part of an answer, whenever it is possible. It focuses on derivatives markets,1 and more specifically on energy derivatives markets.

High Dimensionality in Finance: A Graph-Theory Analysis

In this chapter, we propose a nonconventional methodology, the graph theory, which is especially relevant for the study of high-dimensional financial data. We illustrate the advantages of this method in the context of systemic risk in derivative markets, a main subject nowadays in finance. A key issue is that this methodology can be used in various areas. Numerous applications have now to face the challenge of analyzing gigantic financial data sets, which are more and more frequent. We offer a pedagogical introduction to the use of the graph theory in finance and to some tools provided by this method. As we focus on systemic risk, we first examine correlation-based graphs in order to investigate markets integration and inter/cross-market linkages. We then restrain the analysis to a subset of these graphs, the so-called “minimum spanning trees.” We study their topological and dynamic properties and discuss the relevance of these tools as well as the robustness of the empirical results relying on them.