## Financial Mathematics Seminars - September 27, 2000

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.

### 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 .