Energy and Commodity Finance, Quantitative Financial Modeling, Risk Analysis,
Risk Management, Derivative Security Design, Financial Market Simulation.
- Board Member, Global Commodity Applied Research Digest, J.P.Morgan Center for Commodities
- Energy and Commodity Markets and Products, ESSEC Grande Ecole program.
- Financial Markets, ESSEC Grande Ecole program.
- Commodity Markets and Products, ESSEC MS Financial Engineering (Asian track).
- Options, ESSEC Grande Ecole program.
- Exotic Derivatives, MaFinRisk, Bocconi University (Milan).
- Giovanni Pagliardi (ongoing)
- Lionel Lecesne (ongoing)
- Rachid Id Brik (graduated, Full Marks)
- Javier Pantoja (graduated, Magna cum Laude)
Energy Finance Christmas Workshop 2016 - invited speaker (University of Duisburg-Essen, Dec. 2016), 2016 SIAM Financial Mathematics and Engineering (Austin, Nov. 2016), Energy and Commodity Finance Conference 2016 (ESSEC Paris, Jun. 2016), 2016 Commodity Markets Conference (Hannover, Jun. 2016), 4th Intl. Symposium in Energy & Finance Issues (IPAG Paris, Mar. 2016), Energy Finance 2015 (Cass Business School London, Sep. 2015), French Finance Association AFFI Conference 2015 (Paris, Jun. 2015), 3rd Intl. Symposium in Energy & Finance Issues (IPAG Paris, Mar. 2015), Intl. Ruhr Energy Conference (University of Duisburg-Essen, Mar. 2015), Energy Finance 2014 - invited speaker (Erice, Sep. 2014), 14th Italian Energy Summit - invited speaker (Milan, Sep. 2014), Energy Risk Europe - invited speaker (London, Oct. 2013), Electricity Price Modelling and Forecasting - invited speaker (Berlin, Oct. 2013), AMASES (University of Pisa, Sep. 2011), Commodities Colloquium - invited speaker (EM Lyon, May 2011), International Finance Conference (EGADE Mexico, Nov. 2010), Energy Risk Europe - invited speaker (London, Oct. 2010), Energy Finance 2010 (University of Duisburg-Essen, Oct. 2010), 10th Italian Energy Summit - invited speaker (Milan, Sep. 2010), EURO XXIV Conference (Lisbon, Jul. 2010), Risk Measurement & Control (University La Sapienza Rome, Jun. 2010), International Conference on Quantitative Finance - invited speaker (University of Technology Sydney, Dec. 2009), Environmental and Energy Derivatives - invited speaker (National University of Singapore, Dec. 2009), Quant Risk Europe - invited speaker (London, Nov. 2009), 3rd Risk Management Conference (National University of Singapore, Jul. 2009), European Finance Association (Athens, Aug. 2008), Italian Power Exchange GME (Rome, 2007), 19th International Symposium on Mathematical Programing (Rio de Janeiro, 2006), EFMA (Madrid, 2006), Risk Measurement & Control - invited speaker (Rome, 2006), Energy Commodity Risk (University of London, 2005), European Finance Association (Moscow, 2005), Energy Risk (Erasmus University Rotterdam, 2005), 3rd Bachelier Congress (Chicago, 2004).
Carnegie Mellon University, University of Duisburg-Essen, Universidad Carlos III Madrid, Bocconi University Milan, Banque de France, Politecnico di Milano, Roma Tor Vergata, Universidad de los Andes Bogota, International Energy Agency Paris, Imperial College, Oslo University, Copenhagen Business School, Tilburg University.
Prime Minister Office (Republic of Italy), Central Bank of France, Trafigura Energy Italia, Enel Green Power, Dong Energy, National Science Foundation (US), Natixis, International Energy Agency (IEA), Authority Electricity and Gas, Edison Trading, Gaz de France.
Peer-Reviews for Review of Financial Studies, Mathematical Finance, Journal of Banking and Finance, Applied Mathematical Finance, Journal of Business and Economic Statistics, Energy Economics, Journal of Computational Finance, Journal of Forecasting, Quantitative Finance, Review of Finance, Management Science.
- International Teachers Program – IMD Lausanne, Switzerland.
Italian (mother tongue), English, French, Portuguese, Spanish.
Professor of Finance, ESSEC Business School, Paris - Singapore.
Visiting Fellow, Bocconi University, Milan.
Address: Department of Finance, ESSEC Business School, Av. Bernard Hirsch BP 50105, Cergy; France
Research Areas and Markets
- Price modelling, Security design, Risk measurement.
- Commodity markets, Energy markets, Corporates.
Commodity price modelling, Non-tradable risk management, Price forecasting, Liquidity risk and funds management.
Electricity Forward Curves with Thin Granularity (with R. Caldana and G. Fusai)
European Journal of Operational Research (Forthcoming, 2018)
Abstract: We put forward a constructive definition of electricity forward price curve with cross-sectional timescale encompassing hourly frequency upward. The curve is jointly consistent to both risk-neutral market information, as represented by baseload and peakload futures quotes, and historical market information, as mirrored by periodical patterns exhibited by time series of day-ahead prices. On a methodological ground, we combine nonparametric filtering with monotone convex interpolation in a way that the resulting forward curve is path-wise smooth and monotonic, cross-sectionally stable, and time local. On an empirical ground, we exhibit these features in the joint context of EPEX Spot and EEX Derivative markets. A backtesting analysis assesses the relative quality of our forward curve estimate compared to the benchmark market model of Benth et al. (2007) [Benth, F.E., Koekebakker, S., Ollmar, F. (2007). Extracting and applying smooth forward curves from average-based commodity contracts with seasonal variation. Journal of Derivatives, 15(1), 52-66].
Hedging Size Risk: Theory and Application to the US Gas Market (with R. I. Brik)
Energy Economics (Forthcoming, 2017: DOI version)
Abstract: Many corporate commitments exhibit a combined financial exposure to both market prices and idiosyncratic size components (e.g., volume, load, or business turnover). We design a customized contract to optimally mitigate the risk of joint fluctuations in price and size terms. The hedge is sought out among contingent claims written on price and any quoted index that is statistically dependent on commitment size. Closed-form solutions are derived for the optimal custom hedge pay-off and for the asset holdings of two market strategies, one based on price-linked forwards, the other based on price-linked and index-linked forwards. Analytical hedges are obtained using a stylized lognormal market model. Detailed comparative statics provide a thorough analysis of optimal hedging pay-off functions. Performance assessment is conducted in the context of the US gas market and a prototypical urban region. Results suggest that hedging through suitable custom claims written on price and an additional index significantly outperforms standard price-based as well as mixed price-index forward hedging alternatives. Our optimal custom hedge could be adopted as a benchmark for the relative assessment of any risk management solution.
Static Mitigation of Volumetric Risk (with R. I. Brik)
Journal of Energy Markets 9(2), 2016, 111-150. DOI Version.
Abstract: We consider the problem of designing a financial instrument aimed at mitigating the joint exposure to random price and volume delivery fluctuations of energy-linked commitments. We formulate a functional optimization problem over a set of regular pay-off functions: one is written on energy price, while the other is issued over any index exhibiting statistical correlation to volumetric load. On a theoretical ground, we derive closed-form expressions for both pay-off structures under suitable conditions about the statistical properties of the underlying variables; we pursue analytical computations in the context of a lognormal market model, and deliver explicit formulae for the optimal derivative instruments. On a practical ground, we first develop a comparative analysis of model output through simulation experiments; next, we perform an empirical study based on data quoted at EPEX SPOT power market. Our results suggest that combined price-volume hedging performance improves along with an increase of the correlation between load and index values. This outcome paves the way to a new class of effective strategies for managing volumetric risk upon extreme temperature waves.
Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management (with G. Fusai and M. Cummins)
The Wiley Finance Series (2015), 1-1064.
Description: Gradual deregulation and the resulting increase in diversity and activity have driven the evolution of the traditionally segmented commodity market toward integration, raising important questions about opportunity identification and analysis in multi-commodity deals. This book helps professionals navigate the shift, providing in-depth knowledge, practical advice, and ultimately offering a desktop reference for traders, structurers, risk managers, and academics, who wish to broaden their knowledge base. This manual covers everything one needs to become acquainted with the structure, function, rules, and practices across a wide spectrum of commodity markets, including oil, coal, gas, power, softs, metals, shipping freights, weather derivatives, and FX. A part of the book encompass a large number of quantitative methods and cases about arbitrage valuation, econometric modeling, market structure analysis, contract engineering, and risk management.
Shape Factors and Cross-Sectional Risk (with S. Galluccio and P. Guiotto)
Journal of Economic Dynamics & Control 34, 2010, 2320-2340.
Abstract: Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We propose a theoretical framework supporting that finding, which is based on a notion of “shape factors”. This notion represents cross-sectional risk in terms of stylized analytical deformations experienced by yield curves. We provide an econometric procedure to identify shape factors, and propose a continuous-time yield curve dynamic model driven by these factors. Our proposal consists of a function-valued dynamic term structure model driven by these factors. We also propose and develop the corresponding arbitrage pricing theory. We devise three applications of the proposed framework. First, we derive interest rate derivative pricing formulas. Second, we study the analytical properties exhibited by a finite factor restriction of term structure dynamics that are cross-sectionally consistent with a family of exponentially weighed polynomials. Finally, we conduct an empirical analysis of cross-sectional risk on US swap, Euro bond and oil price data sets. Results support our conclusion that shape factors outperform the classical yield/price factors (i.e., level, slope, and convexity) in explaining the underlying market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data, whether it be price curves, option implied volatility smiles, or cross-sections of equity returns.
Encyclopedia of Quantitative Finance, Wiley & Sons, 2010, 298-303.
Re-edited in Portoguese as: Modelos Dinamicos em Financas: O Caso dos Modelos de Determinação do Preço de Commodities
In: R. Pereira, A Dinâmica nas Ciências Econômicas e Empresariais - Contributos para uma Visão Abrangente. Escolar Editora, Lisboa, 2010, 183-194.
Abstract: Arbitrage models of commodity prices are relative pricing devices. They allow market operators to evaluate commodity-linked securities in terms of quoted commodity prices or indices. Model instances differ in terms of underlying primitives, from which prices of more complex positions can be derived, and in the way the stochastic dynamics of these building blocks is described, namely through structural elements (e.g., price drift, volatility, and jump components) and driving noise terms.
Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets (with M. Marena and G.Fusai)
Journal of Banking and Finance 32, 2008, 2033–2045.
Abstract: We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61–73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.
Implementing Models in Quantitative Finance (with G. Fusai)
Springer Finance, 2008, 1-607.
Abstract: This book puts numerical methods into action for the purpose of solving concrete problems arising in quantitative finance. Part one develops a comprehensive toolkit including Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques. The content originates from class notes written for courses on numerical methods for finance and exotic derivative pricing held by the authors at Bocconi University since the year 2000. Part two proposes eighteen self-contained cases covering model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation and model calibration. It encompasses a wide variety of problems arising in markets for equity, interest rates, credit risk, energy and exotic derivatives. Each case introduces a problem, develops a detailed solution and illustrates empirical results. Proposed algorithms are implemented using either Matlab® or Visual Basic for Applications® in collaboration with contributors.
Understanding the Fine Structure of Electricity Prices (with H. Geman)
The Journal of Business 79(3), 2006, 1225-1261.
Abstract: This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a “jump-reversion” component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets.
A New Measure of Cross-Sectional Risk and its Empirical Implications for Portfolio Risk Management (with S. Galluccio)
Journal of Banking and Finance 30, 2006, 2387–2408.
Abstract: Litterman et al. [Litterman, R., Scheinkman, J., Weiss, L., 1991. Volatility and the yield curve. Journal of Fixed Income 1 (June), 49–53] and Engle and Ng [Engle, R.F., Ng, V.K., 1993. Time varying volatility and the dynamic behavior of the term structure. Journal of Money, Credit and Banking 25(3), 336–349] provide empirical evidence of a relation between yield curve shape and volatility. This study offers theoretical support for that finding in the general context of cross-sectional time series. We introduce a new risk measure quantifying the link between cross-sectional shape and market risk. A simple econometric procedure allows us to represent the risk experienced by cross-sections over a time period in terms of independent factors reproducing possible cross-sectional deformations. We compare our risk measure to the traditional cross-yield covariance according to their relative performance. Empirical investigation in the US interest rate market shows that (1) cross shape risk factors outperform cross-yield risk factors (i.e., yield curve level, slope, and convexity) in explaining the market risk of yield curve dynamics; (2) hedging multiple liabilities against cross-shape risk delivers superior trading strategies compared to those stemming from cross-yield risk management.
Flexible-Rate Mortgages (with A. Moro)
International Journal of Business 11(2), 2006, 143-157.
Abstract: We propose a model for the endogenous determination of an optimal refinancing policy for mortgage loans under limited refinancing opportunities. Transaction costs are also included in the analysis. A detailed examination of the optimal exercise distributions sheds light on the impact of contract features on the average prepayment behavior in mortgage-backed securities.
Theory and Calibration of HJM with Shape Factors (with P. Guiotto)
In: Geman H., Madan, D., Pliska, S.R., Vorst, T., Mathematical Finance, Springer Finance, 2001, 407-426.
Abstract: We construct arbitrage-free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finite-dimensional space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the development of a historical-implicit hybrid calibration procedure for our shape factor model. In this context, we also derive a pricing formula for caplets.
Professional Journal Contributions
Monetary Measurement of Risk: a Critical Overview - Part II: Coherent Measures of Risk (with L. Lecesne)
Argo Review, Issue 3 (Summer), 13-18.
Abstract: In Lecesne and Roncoroni (2014), we introduce the notion of monetary measure of risk borne by any financial claim. Our presentation moves from general definitions to concrete instances, including the benchmark measure Value-at-Risk (VaR). Part II develops a treatment of the class of coherent (monetary) measures of risk put forward by Artzner et al. (1999). Our goal is to illustrate the main features of this class of measures in light of application to practical cases. In this respect, we put our focus on the ambiguity of the term “coherent” and show that the connotation of consistency it naturally embeds is more an issue of lexical interpretation than actual meaning. As an example, we show that lack of subadditivity of VaR (which prevents from it to being a “coherent” measure of risk) is more a desirable property than a drawback, as is claimed in most of existing sources in the specialized literature.
Monetary Measurement of Risk: a Critical Overview - Part I: General Definitions and Value-at-Risk (with L. Lecesne)
Argo Review, Issue 1 (Winter), 2014, 67-72.
Abstract: The simplest and perhaps most significant definition of risk relates the term to any sort of “exposure to uncertainty” (Leppard (2005)). We hereby focus on risk affecting physical and financial asset values and related cash flows, what we refer to as financial risk. Our starting point is the notion of position intended as a set, possibly a singleton, of assets generating financial cash flows as a primary or secondary output. Assets of this kind include financial securities, loans, commodity portfolios, commercial agreements, and real assets. Our goal is to develop a critical introduction to the class of monetary measures of risk, i.e., cash-valued metrics of risk affecting a position under consideration.
Argo Review, Issue 1 (Winter), 2014, 47-56.
Abstract: We derive a closed-form formula for the fair value of call and put options written on the arithmetic average of security prices driven by jump diffusion processes displaying (possibly periodical) trend, time varying volatility, and mean reversion. The model allows one for jointly fitting quoted futures curve and the time structure of spot price volatility. Our result extends the no jump case put forward in [Fusai, G., Marena, M., Roncoroni, A. 2008. Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets. Journal of Banking and Finance 32 (10), 2033-2045]. A few tests based on commodity price data assess the importance of introducing a jump component on the resulting option prices.
LesEchos.fr, 23 Novembre 2012.
Abstract: Les énergies représentent une composante fondamentale dans la production mondiale. Comprendre l'évolution de la composante énergétique globale est d’autant plus nécessaire aujourd’hui que les systèmes de production et de consommation mondiales sont devenu extrêmement énergivores. Ceci génère une croissance des prix dans le temps et les prix élevés ont poussé à rechercher de nouveaux moyens alternatifs de production énergétique.