SCIENTIFIC PROGRAMS AND ACTIVITIES

September 17, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Focus Program on Commodities, Energy and Environmental Finance


Focus Program Visitors Seminars
Organizing Committee
Mike Ludkovski (UC Santa Barbara)
, Ronnie Sircar (Princeton)

Time Talk Title and Abstract

Tuesday, Aug 6
2:00pm

Matheus Grasselli (slides)
Energy, Finance, and Macroeconomics

Like many other areas in financial mathematics, the study of commodities, energy, and environmental finance developed as a branch of financial economics, and is therefore based on equilibrium, rational expectations, representative agents, and other notions from mainstream economics. Since the 2007-08 financial crisis, however, these shaky foundations for the subject have been vigorously attacked, and several alternative views gained prominence.
In this talk I'll informally review some strands of heterodox macroeconomics, with emphasis on the work of Hyman Minsky and Wynne Godley. In particular, I'll describe the framework of stock-flow consistent models and give an explicit example related to Green Jobs based on a recent proposal by Antoine Godin (2012).

Wednesday, Aug 7
2:00pm

Matt Davison, University of Western Ontario (slides)
Management of Wind Energy with Storage: Structural Implications for Policy and Market Design

The generation resource uncertainty induced by significant wind capacity raises concerns about grid security, price stability and revenue adequacy. One of the most promising solutions is the use of utility scale energy storage, though the question of general implementation of this strategy remains unanswered. In this talk, I present a simplified model to show that there exist simple rules governing optimal bidding and energy storage rules from a hybrid wind-storage system. The heuristics developed consider the combination of storage efficiency, electricity price and shortfall penalty and wind forecast characteristics to guide the decision of whether to bid energy into the electricity market.

We develop the optimal strategy for use of a simplified system of an energy storage unit with a wind generator. The solution is analyzed as a dynamic program, in a simplified framework over a multi-period planning horizon. The analysis of the solution under all regimes yields insightful structural solutions regarding the conditions under which the wind generator should bid into the energy market and when they should not.

For the simple case in which each period is, independent of previous periods, equally likely to be sufficiently windy to generate power, we rigorously prove that for all combinations of wind probability, shortfall penalty, and round trip efficiency, it is always optimal to bid energy into the market when storage is full, and always optimal to avoid a shortfall penalty by using stored energy, regardless of the magnitude of the penalty and regardless of the time remaining in the planning horizon. However, when stored energy is unavailable, the optimal bid rule depends on the penalty size as a function of storage loss characteristics, wind probability, and time remaining in the planning horizon. While analytic results are not available in the more complicated case of a time varying probability of wind, numerical results show results which, while broadly consistent with the constant wind probability case, vary from that case in interesting ways.

The results of this paper provide insight into the implications of forecast accuracy and market design on the need for storage. This analysis allows additional conclusions to be drawn about the value of various storage technologies based on their capacity and efficiency characteristics. However, the most important contribution of this work is the understanding of the importance of market penalties in encouraging participants to either improve forecasting ability or, perhaps more realistically, contract storage to mitigate shortfall risk. This is joint work with Lindsay Anderson (Cornell) and Natasha Burke (Western).

Monday, Aug 12
3:30pm

Rene Aid, EDF R&D and Finance for Energy Market Research Centre
A probabilistic numerical method for optimal multiple switching problem applied to investments in electricity generation

Free boundary problems naturally arise when dealing with investment decisions in electricity generation. The problem is so complex in terms of operating constraints, alternatives and random factors that simplifications have to be made. The common approach in the electric industry is still to rely on generation expansion planning methods. Those models use a detailed representation of the electric system to provide a single policy that will satisfy the future demand. Thanks to the development of real options methodology, alternative models have been developed in the economic and mathematical literature. Those simplified models provide insights of the optimal investment strategy in electricity generation.

In this talk, we will first provide a review of the most salient examples of those models. In particular, we will see that, although they provide an understanding of the investment dynamic, they are limited to small dimension. So, we will show how the progress made in the last decade by numerical methods for optimal switching problem can be used to overcome the dimensionality issue. We will give the example of a high dimensional electricity generation investment model. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself constructed according to an extended structural model. In particular, it is a function of the random processes as well as the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension 8, i.e. with 2 different technologies and 6 random processes. This talk is based on a joint work with Luciano Campi, Nicolas Langrene and Huyen Pham.

Tuesday, Aug 13
3:30pm

Ivar Ekeland, UBC and Paris Dauphine (slides)
No turning back: growth theory and sustainable developmen

We present a model for sustainable development, which is an extension of the classical Ramsey model for economic growth. The extension consists in adding to the criterion of the representative agent a term, due to Chichilnisky, which represents concern for the distant future. We show that, in addition to the business as usual strategy, corresponding to the optimal solution in the Ramsey model, with no concern for the future, there are additional strategies, but that they cannot build up natural capital once it has been destroyed.
Monday, Aug 19
2:00pm

Lane P. Hughston, University College London (slides)
Social Discounting and the Long Rate of Interest

The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which although undoubtedly correct has been regarded by many as counterintuitive and even pathological, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in the setting of modern interest rate theory, and show that if the long simple interest rate (or Libor rate) is finite, then this rate (unlike the zero-coupon rate) acts viably as a state variable, the value of which can fluctuate randomly in line with other economic indicators. New interest rate models are constructed, under this hypothesis, that illustrate explicitly the good asymptotic behaviour of the resulting discount bond system. The conditions necessary for the existence of such hyperbolic long rates turn out to be those of so-called social discounting, which allow for long-term cash flows to be treated as broadly as those of the short or medium term. As a consequence, we are able to provide a consistent arbitrage-free valuation framework for the cost-benefit analysis and risk management of long-term social projects, such as those associated with sustainable energy, resource conservation, space exploration, and climate change. (Joint work with Dorje C. Brody, Brunel University. Paper available at arXiv:1306.5145)
Wednesday, Aug 21
2 p.m.
John Chadam, University of Pittsburgh
The inverse boundary crossing problem for diffusions

A summary of our work on the inverse boundary crossing problem for diffusions will be presented. To begin, the direct and inverse problems will be described in their probabilistic, PDE and integral equation settings. Our previous results on the existence and uniqueness of the solution to the inverse problem in the PDE setting will be outlined. More recently a verification theorem was established showing that this solution solves the probabilistic version of the problem. Results on the initial behavior and continuity of the boundary will be described. Finally, a numerical scheme based on the equivalent integral equation formulation of the problem will be discussed. (Joint work with Xinfu Chen, Lan Cheng & David Saunders)

Thursday, Aug 22
2 p.m.
Tim Leung, Columbia University
Leveraged ETFs and their Options

We discuss the performance of leveraged exchanged-traded funds (LETFs) and the implied volatilities of LETF options, with an emphasis on the role of different leverage ratios. First, we examine the empirical returns and implied volatility surfaces for LETFs based on the S&P 500 index, and introduce the concept of "moneyness scaling" to enhance their comparison with non-leveraged ETF implied volatilities. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. Our result is applied to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage reflected in the different products, long and short with leverage ratios two times and three times.

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