Automatic adjoint differentiation for mean squared error involving expectations

• Autor(a) principal: Brito, José Nuno Catarino
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/37355
• topic: Diferenciação automática adjunta; Computação em paralelo; Simulação de Monte-Carlo; Opções europeias; Erro quadrático médio; C++

This dissertation will have as an objective, explain how to calculate gradients of Mean Squared Error, (...), since it's applied in calibration methods of stochastic models, using the Automatic Adjoint Differentation and parallelization. With the involviment of mean values, the application of the Monte-Carlo Simulation will be needed to approximate possible expected values as well as, distinct and appropriate estimation methods for the computation of its correspondents partial derivaties. Therefore, in this document, will be initialized with the introduction of certain concepts needed, like the Automatic Adjoint Differentiation, the Monte-Carlo Simulation, as well as, Call Options of European Options since, will be used, for a pratical case, a simple stochastic model of European Call Options applying the differentiation for a certain group of parameters. Finally, such concepts introduzed previously, will be applied for the primary objective, analizing the theoretical and pratical results from which you can withdraw with the different estimation methods applied.