Método dos elementos finitos baseado em polinómios de Hermite cúbicos, para resolução da equação de Black-Scholes não linear com opções europeias
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https://doi.org/10.22481/intermaths.v2i2.9481Palavras-chave:
Nonlinear Black-Scholes, Finite Element Method , Crank-Nicolson, Hermite PolynomialsResumo
Foi desenvolvido um algoritmo numérico para resolver uma equação diferencial parcial generalizada de Black-Scholes, que surge na precificação de opções europeias, considerando os custos de transação. O método Crank-Nicolson é usado para discretizar no tempo e o método de interpolação cúbica de Hermite para discretizar no espaço. A eficiência e precisão do método proposto são testadas numericamente e, os resultados confirmam o comportamento teórico das soluções, que também se encontra em boa concordância com a solução exata.
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