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Mathematics for Finance and Economics


HERA TRADING s.r.l.

Courses, professors and summaries

A course on commodities - C1 Course 2 (7 hours)
prof. Helyette Geman

Summary:
  • Part One
    • Fundamentals of Spot and Futures Commodities Markets
    • Shipping and Freight
    • Theory of Storage and Inventory; the extreme case of electricity
    • Stochastic Modeling of commodity forward curves
    • The Borovkova-Geman model: applications to the Natural Gas and Crude Oil forward curves
  • Part Two
    • Options on Spot and Futures commodities
    • Asian options in Commodity Markets: the mathematical challenges
    • Investing in Commodities: from Indexes to ETFs and Structured Notes
References:
  • Understanding the Fine Structure of Electricity Prices - Geman, Roncoroni
  • Fundamentals of Electricity Derivatives
  • Energy Commodity Prices: Is Mean-Reversion Dead?
  • Soybean Inventory and Forward Curve Dynamics

    Stochastic modelling of electricity markets - C2 Course 1 (8 hours)
    prof.     Fred Espen Benth

    Summary:
    Electricity markets have in the last two decades been liberalized world-wide. Since electricity is a non-storable commodity, several challenging questions appear when analysing these markets from a quantitative point of view. The electricity spot price has distinct features like seasonality and spikes, where prices may soar several magnitudes above "normal levels" in short time. Due to the non-storability, the connection between spot and forward/futures contracts are not clear, since we cannot argue using hedging arguments like in other commodity markets. Furthermore, the futures contracts have settlement over a period rather than at a fixed delivery time, creating additional technical complications. In this series of lectures we will introduce different models for the electricity spot price using mean-reversion processes driven by jumps. Further, we discuss different approaches to modelling electricity futures prices. A natural approach is to derive the futures price from the spot using the "market price of risk". As an alternative, we look at a certainty equivalence principle for deriving prices, which in simple models can explain the changing sign of the risk premium frequently observed in the electricity markets. Finally, we consider an approach which includes forward information in the derivation of futures prices. Here we encounter theory based on "enlargement of filtrations" in stochastic analysis. All our analysis will be accompanied by empirical investigations.
    • An introduction to electricity markets
    • Electricity spot price models
      • Mean-reversion models with jump processes
      • Arithmetic and geometric models
      • Estimation and simulation issues
    • Modelling electricity futures prices
      • The approach based on "market price of risk" and Esscher transformation
      • The certainty equivalence principle and explaining the sign of the risk premium
      • Electricity futures prices based on forward information

    Helyette Geman
    Helyette GEMAN is a Professor of Finance at Birkbeck, University of London and ESSEC Graduate Business School. She is a graduate of Ecole Normale Superieure in mathematics, holds a Masters degree in theoretical physics and a PhD in mathematics from the University Pierre et Marie Curie and a PhD in Finance from the University Pantheon Sorbonne. Professor Geman has been a scientific advisor to a number of financial institutions and major energy and mining companies for the last 15 years, covering the spectrum of interest rates, oil, natural gas and metals. She was previously the head of Research and Development at Caisse des Depots. She has published more than 90 papers in major finance journals including the Journal of Finance, Mathematical Finance, Journal of Financial Economics, Journal of Banking and Finance and Journal of Business. She has also written a book entitled Insurance and Weather Derivatives and is a Member of Honor of the French Society of Actuaries. Professor Geman's research includes asset price modelling using jump-diffusions and Levy processes, commodity forward curve modelling and exotic option pricing for which she won the first prize of the Merrill Lynch Awards. She was named in 2004 in the Hall of Fame of Energy Risk. Her latest book Commodities and Commodity Derivatives was published by Wiley Finance in January 2005. Helyette Geman is a Member of the Board of the UBS-Bloomberger Commodity Index.

    Fred Espen Benth
    Fred Espen Benth is professor in financial mathematics and deputy manager at the Centre of Mathematics for Applications (CMA), University of Oslo. His areas of interests include quantitative analysis of energy and weather markets. Benth has numerous publications in scientific journals like for instance Mathematical Finance, Finance and Stochastics, Quantitative Finance, Applied Mathematical Finance and Journal of Derivatives, and is associate editor of the journal Mathematical Methods in Operations Research. Apart from his scientific activities, Benth is consulting the energy, finance and insurance industry in Norway. Before becoming a professor, he worked three years as a consultant for the oil industry at the Norwegian Computing Centre and as a scientist at the universities in Mannheim, Aarhus and Trondheim.


    (http://folk.uio.no/fredb/)