July 17, 2024

Financial Mathematics Seminars - September 27, 2000

Dynamics of Electricity Spot and Forward Prices and the Valuation of Contingent Claims
Raymond Ross - Ontario Power Generation

In the wake of deregulating power markets throughout the world, demand for power risk management vehicles is increasing. The majority of modeling efforts undertaken to price and hedge such instruments has tended to focus on the behaviour of the spot price of electricity. Since electricity cannot effectively be stored, positions in spot cannot be used to hedge a generic contingent claim on power. In reality, it is the forward market in power that affords hedging instruments, and what is required is a dynamic model of forward prices.

In this talk, we will discuss the general nature of power contingent claims, the qualitative behaviour of spot prices, and a general framework linking spot price behaviour to arbitrage-free models of power forwards.

Optimal Execution with Liquidity Risk

Robert Almgren, University of Toronto

In carrying out a large portfolio transaction, a trader must balance the liquidity premium he must pay to trade rapidly, against the uncertainty of future prices to which he is exposed by trading slowly. Using a simple model for how trading moves prices, and using a simple utility function formulation for balancing risk against known costs, we apply the calculus of variations to determine an optimal trading strategy in terms of a few market parameters. We argue that these solutions are a realistic mathematical formulation of traders' intuition about optimal trading. We examine actual US stock market data to estimate the parameters in our model, and show that the time scales characterizing optimal liquidation strategies vary by several orders of magnitude across the market.

Joint work with Neil Chriss
Copies of the working paper are available here .