Franck Raynaud

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.

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.

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.

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.