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Partial differential equations for pricing in carbon markets

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Detalhes bibliográficos
Resumo:In this thesis we present a numerical pricing method for allowance certificates in the European Union Emissions Trading Scheme (EU ETS). The presented approach lies inbetween an equilibrium model that are already widely used in this field and a simplistic risk-neutral model. Using an exogenously stated demand process for a polluting good, it gives a causal explanation for the accumulation of CO2 emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO2. We develop a Forward-Backward Stochastic Differential Equation (FBSDE) and numerically present a Crank-Nicolson approximation scheme for the associated semilinear Partial Differential Equation (PDE) for the price of the allowance certificate while also showing that the derivatives specified on the allowance certificate satisfy a linear Partial Differential Equation.
Autores principais:Cavalheiro, Joaquim Miguel Couto dos Santos
Assunto:Semilinear PDE Forward-Backward Stochastic Differential Equation Emissions Market Allowance Certificates Cap-and-trade
Ano:2022
País:Portugal
Tipo de documento:dissertação de mestrado
Tipo de acesso:acesso aberto
Instituição associada:Universidade de Lisboa
Idioma:inglês
Origem:Repositório da Universidade de Lisboa
Descrição
Resumo:In this thesis we present a numerical pricing method for allowance certificates in the European Union Emissions Trading Scheme (EU ETS). The presented approach lies inbetween an equilibrium model that are already widely used in this field and a simplistic risk-neutral model. Using an exogenously stated demand process for a polluting good, it gives a causal explanation for the accumulation of CO2 emissions and takes into account the feedback effect from the cost of carbon to the rate at which the market emits CO2. We develop a Forward-Backward Stochastic Differential Equation (FBSDE) and numerically present a Crank-Nicolson approximation scheme for the associated semilinear Partial Differential Equation (PDE) for the price of the allowance certificate while also showing that the derivatives specified on the allowance certificate satisfy a linear Partial Differential Equation.