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Risk premium and stochastic equilibrium in generation capacity expansion models

Presented by: 
Yves Smeers
Thursday 21st March 2019 - 09:00 to 10:00
INI Seminar Room 1
Investment in new capacities is most often based on a Weighted Average Cost of Capital where the cost of equities is derived from the Capital Asset Pricing Model (the cost of debt following a different logic). While a single corporate discount rate was most often used in the past, differentiated discount rates reflecting elements such as technology and country risks are now more used. These introduce undesirable arbitrage phenomena in standard capacity expansion model interpreted as market simulation models. We discuss three types of differentiated discounting namely the standard (often based on CAPM) exogenous discount rate, the more general stochastic discount rate and the endogenous discount rate derived from risk functions possibly with hedging instruments. The three approaches are cast in a unifying risk premium equilibrium formulation where arbitrage phenomena are eliminated. The models are of the complementarity form and can be handled through splitting algorithms. We report numerical results for medium size problems adequate for industrial use.  Convergence is based on an (often implicit) assumption of monotonicity that is not necessarily satisfied for endogenous discount rates. We briefly discuss the different equilibrium that can arise when this assumption is not satisfied.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons