FINANCIAL MATHEMATICS ACTIVITIES

Financial Mathematics Seminars - February 28, 2001

Abstracts

Discrete and Continuous-Time Approaches to Modelling Spot Electricity Prices

Matt Davison, University of Western Ontario

The current continent-wide deregulation of the electrical power marketplace brings with it the challenge of valuing options to trade spot electrical power. In order to do this, a stochastic model for spot electricity prices and a means for accounting for risk in the discounting of cash flows are required. Once those are in hand, realistic electrical power options may be priced. In this talk I present some approaches taken by our group to these problems.

The bulk of our effort so far has been in the construction of stochastic electricity price models. Electrical power is a unique commodity. It is essential and cannot be stored, so "spikes", in which spot electricity prices rise by large factors, are often observed. Electrical power markets have only been deregulated in recent years, so price time series are relatively short. Furthermore, every regional market has its own special characteristics, making calibration of models across regions dangerous. Mitigating these problems to a certain extent is the availability of engineering data about the operation of electrical power markets - both in terms of the main demand drivers (weather, diurnal variability) and in terms of the main supply drivers (plant outages). Also available is a great deal of historical "load" information which describes how much power was actually generated and consumed in given time intervals. Our models are more dependent on engineering lore and load data than they are on historical price data.

We have constructed two classes of model. The first is a discrete-time model designed to "get the spikes right". This is a "switching" or "mixture of distributions" model. The second, continuous-time model, simulates spikes without resorting to Poisson jumps. We also present some preliminary work on pricing options with these models.

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Market Imperfections, Investment Optionality and Default Spreads

Stathis Tompaidis, McCombs School of Business, University of Texas at Austin

We present a model for the valuation of risky debt that accounts for the endogeneity of the borrower's investment choice as well as possible borrowing constraints. The model also extends previous research by assuming that changes in the cash flows generated by the loan's collateral have both permanent and temporary components and illustrates why this is relevant in a setting with market imperfections. The paper presents numerical simulations that allow us to quantify the extent to which investment flexibility, incentive problems and credit constraints affect borrowing rates.

Joint with Sheridan Titman and Sergey Tsyplakov, University of Texas at Austin.