Energy and Power Risk Management: New Developments in Modeling, Pricing and Hedging (Wiley Finance) [Hardcover]

In chapter 5 the author presents techniques for energy modeling that go beyond the used of the convenience yield by using forward pricing techniques. The goal is to describe the dynamics of future contract prices that takes into account the correlations with other futures, and not on the price evolution of a single contract. Thus it is the `forward curve' that is relevant for obtaining a useable model for derivative cash flow. The HJM model is presented as one of these, with changes in the forward curve over a particular time interval represented as a linear combination of random perturbations. For energy markets, each perturbation is specified by a deterministic shape function multiplied by a Gaussian factor. The unobservability of the factors determining the forward curve evolution makes the use of historical data mandatory if the parameters are to be estimated. But lack of sufficient historical data and its nonstationarity complicate this estimation. The authors discuss the Schwartz-Smith multi-factor model as an example of a forward curve dynamics model and give some solutions. They then move on to a model that specifies the dynamics for only the contracts that are actually traded, which in the literature are called `market models.' The model they actually discuss is a multivariate geometric Brownian motion representation of the forward curve dynamics, where the volatility and drift functions are linear functions of the forward prices. The authors then derive the `discrete string models', where it is assumed that the number of factors is equal to the number of contracts, and the random factors are governed by ordinary Brownian motion. String models are represented as having the advantage of being able to directly observe the factors in the historical data. The authors apply string models to multi-commodity cases, and discuss an example for monthly forward prices. They show how to match the current forward curve, the option prices, and the correlation structure for this model.

The discussion in chapter 7 revolves around finding better models for the dynamics of power prices that capture the special properties of energy prices, such as mean reversion and seasonality, and the need for stable models. They therefore introduce `hybrid models', which they claim give a more natural representation of the dynamics of power prices, make use of nonprice forward-looking information, and can take the historical data on power prices and then extend it to information on fuel prices, outages, etc. The construction of these models is based on the use of nonlinear transformations on a collection of random variables. The random variables are essentially the system demand, natural gas and oil price, outages, emission prices, and weather at a particular time. The power price then can be written as a function of the dynamics of these factors, the latter written by the authors in terms of the corresponding tradables. Recognizing that hedging cannot be done on some of these factors, they adjust the power price formula so that the power tradables, i.e. the forwards and option prices, are exactly matched. This matching transformation is chosen so that if the forward contracts and options are priced using the adjusted formula, one recovers the exact current prices. The model, as the authors summarize it, is an attempt to explain the behavior of the tradables in terms of the evolution of the underlying factors and static adjustments to the terminal probability distribution. Historical information on the tradables and spot products is not used to calibrate the model, but it is used to validate the model. The authors distinguish between `reduced-form' hybrid models, where the transformation is calibrated from the historical prices, and `fundamental' hybrid models, where the transformation is calibrated from the market structure and is only tested on the historical prices. The authors discuss an example of a reduced-form hybrid model that is heavily parametrized, but has the advantage of using price data more efficiently. The rest of the chapter concentrates on fundamental hybrid models, with the author first discussing how power prices are formed in competitive markets. They consider a typical pool market, with the price determined via auction mechanisms. The authors then try to identify and characterize the underlying random variables that actually affect power prices. The time series for the price of power is written in terms of the demand using a `bid stack' function. The bid stack function is approximated by a `generation stack' that is found for a given time by sorting generation units by their generation costs. This approximation is checked by comparing the marginal generation costs generated by the generation stack with the distribution of power prices determined by the time series via the bid stack. There should be agreement in both approaches between the higher order moments. This comparison forms the basis of the authors' hybrid approach to modeling power prices. A transformation is found which relates the marginal generation costs to the distribution of power prices with the requirement that the prices of market instruments used for calibration are matched, and the higher moments are (approximately) preserved. The transformation is not unique, and in fact a family of transformations induced by the multiplication and stack scaling operators can be found.

To me, the greatest strength of the book lies in its fairly detailed analysis of what DOESN'T work, i.e. why common models and methods from the financial and other commodity realms can not be successfully grafted onto the energy market without risking significant valuation and cash flow prediction errors. The hybrid model they formulate towards the end of the book is very similar to Skantze and Ilic (2001). The departure from most previous models is that they attempt to use the markets to formulate and calibrate the structure instead of relying too much on past historical price/load data, which without some empirical understanding of the underlying processes, is fraught with danger due to rapidly evolving nature of the power market (or at least once rapidly evolving--it seems to be a little static at the moment).

Some familiarity with the market and stochastic/statistical mathematics is assumed. References to specific topics and more in depth analysis of particular subjects are good. The authors have a grip on real-world trading, risk, and cashflow issues, which makes this a useful reference for just about anyone associated with those aspects of the power market. I recommend it.