Liquidity risks on power exchanges

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.illiquidity, electricity, power exchange, artitrage, generalized Nash Equilibrium, equilibrium based model, coherent risk valuation

Coherent Price Systems and Uncertainty-Neutral Valuation

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem, see Harrison and Kreps (1979). We establish a microeconomic foundation of sublinear price systems and present an extension result. In this context we introduce a prior dependent notion of marketed spaces and viable price systems. We associate this extension with a canonically altered concept of equivalent symmetric martingale measure sets, in a dynamic trading framework under absence of prior depending arbitrage. We prove the existence of such sets when volatility uncertainty is modeled by a stochastic differential equation, driven by Peng's G-Brownian motions

Structuring Exotic Options Contracts on Water to Improve the Efficiency of Resource Allocation in the Water Spot Market

With the current drought in South-Eastern Australia highlighting the scarcity and value of inland Australia’s water resources, focus turns to how these resources can be allocated more efficiently. The first major step was taken almost a decade ago with the separation of land and water property rights allowing openly traded water markets. This study assesses the potential economic benefits that options contracts bring to the water market in the Murray Valley water market. Exotic call options are estimated using both Black-Scholes and skewness-and-kurtosis-amended Black-Scholes financial option pricing methods that are based on three years of data on water prices. While the presence of options would result in significant economic benefits in the more efficient trade of water on the open market for lower-value crops, there were mixed results from the attempt to price such options.options, skewness-and-kurtosis-amended Black-Scholes model, water, Environmental Economics and Policy, Financial Economics, Research Methods/ Statistical Methods, Resource /Energy Economics and Policy,

Measuring and managing the credit exposure of derivatives portfolios

CONCLUSION The analysis of the exposure measurement problem has shown that the proper measurement of counterparty exposure for portfolios of derivatives transactions is a complex task that cannot be performed without making a lot of simplifying assumptions. Because of the complicated interaction of correlation effects and offsettings from different transactions, the single transaction framework which is currently used by most banks is definitely not capable of accurately determining the portfolio credit risk. When simulation techniques are applied to estimate exposure, the accuracy of exposure estimations can be increased significantly. However, a lot of modelling choices has to be made concerning the valuation of transactions and the stochastic model of underlying market rates. Because the system has to make projections of market rates into the far future, the choice of an appropriate stochastic model for market rate dynamics is crucial in order to prevent unreasonable scenarios. The predominant application of models based on Brownian Motion in today’s bank risk management therefore leads to questionable results in respect to derivatives exposure evaluation

Utility indifference pricing with market incompleteness

Utility indifference pricing and hedging theory is presented, showing how it leads to linear or to non-linear pricing rules for contingent claims. Convex duality is first used to derive probabilistic representations for exponential utility-based prices, in a general setting with locally bounded semi-martingale price processes. The indifference price for a finite number of claims gives a non-linear pricing rule, which reduces to a linear pricing rule as the number of claims tends to zero, resulting in the so-called marginal utility-based price of the claim. Applications to basis risk models with lognormal price processes, under full and partial information scenarios are then worked out in detail. In the full information case, a claim on a non-traded asset is priced and hedged using a correlated traded asset. The resulting hedge requires knowledge of the drift parameters of the asset price processes, which are very difficult to estimate with any precision. This leads naturally to a further application, a partial information problem, with the drift parameters assumed to be random variables whose values are revealed to the hedger in a Bayesian fashion via a filtering algorithm. The indifference price is given by the solution to a non-linear PDE, reducing to a linear PDE for the marginal price when the number of claims becomes infinitesimally small