A general methodology to price and hedge derivatives in incomplete markets

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox-Ross-Rubinstein and Black-Scholes in the complete markets case and the Schweizer and Bouchaud-Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.Comment: 24 pages, LaTeX, epsfig.sty, 5 eps figures, changes in the presentation of the method, submitted to International J. of Theoretical and Applied Financ

Risk management in electricity markets: hedging and market incompleteness

The high volatility of electricity markets gives producers and retailers an incentive to hedge their exposure to electricity prices by buying and selling derivatives. This paper studies how welfare and investment incentives are affected when markets for derivatives are introduced, and to what extent this depends on market completeness. We develop an equilibrium model of the electricity market with risk-averse firms and a set of traded financial products, more specifically: forwards and an increasing number of options. Using this model, we first show that aggregate welfare in the market increases with the number of derivatives offered. If firms are concerned with large negative shocks to their profitability due to liquidity constraints, option markets are particularly attractive from a welfare point of view. Secondly, we demonstrate that increasing the number of derivatives improves investment decisions of small firms (especially when firms are risk-averse), because the additional financial markets signal to firms how they can reduce the overall sector risk. Also the information content of prices increases: the quality of investment decisions based on risk-free probabilities, inferred from market prices, improves as markets become more complete Finally, we show that government intervention may be needed, because private investors may not have the right incentives to create the optimal number of markets.

Market completeness: how options affect hedging and investments in the electricity sector.

The high volatility of electricity markets gives producers and retailers an incentive to hedge their exposure to electricity prices by buying and selling derivatives. This paper studies how welfare and investment incentives are affected when an increasing number of derivatives are introduced. It develops an equilibrium model of the electricity market with risk averse firms and a set of traded financial products, more specifically: a forward contract and an increasing number of options. We first show that aggregate welfare (the sum of individual firms' utility) increases with the number of derivatives offered, although most of the benefits are captured with one to three options. Secondly, power plant investments typically increase because additional derivatives enable better hedging of investments. However, the availability of derivatives sometimes leads to ‘crowding-out’ of physical investments because capital is being used more profitably to speculate on financial markets. Finally, we illustrate that players basing their investment decisions on risk-free probabilities inferred from market prices, may significantly overinvest when markets are not sufficiently complete.