A new finite difference method for pricing and hedging interest rate derivatives : comparative analysis and the case of the idi option

• Ano de defesa: 2015
• Autor(a) principal: Silva, Allan Jonathan da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Laboratório Nacional de Computação Científica; Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA); Brasil; LNCC; Programa de Pós-Graduação em Modelagem Computacional
• Palavras-chave em Português: Engenharia financeira; Taxa de juros; Administração de riscos; Financial engineering; Interest rates; Risk management; CNPQ::CIENCIAS SOCIAIS APLICADAS::ECONOMIA::METODOS QUANTITATIVOS EM ECONOMIA::METODOS E MODELOS MATEMATICOS, ECONOMETRICOS E ESTATISTICOS
• Link de acesso: https://tede.lncc.br/handle/tede/208

We propose a second order accurate numerical finite difference method to replace the classical schemes used to solving PDEs in financial engineering. The motivation for doing so stems from the accuracy loss while trying to stabilize the solution via the up-wind trick in the convective term as well as the fact that spurious oscillation solutions occur when volatilities are low. This is actually the range that we commonly observe in the interest rate markets. Unlike the classical schemes, our method covers the whole spectrum of volatilities in the interest rate dynamics. We compare the analytical and numerical results by both pricing and hedging a variety of fixed income financial contracts to show that the method we developed is reliable and highly competitive. The method adapts well to exotic interest rate derivative securities, including a path-dependent derivative named IDI (the Brazilian Interbank Deposit Rate Index) option. The method highlights the use of the realistic discretely compounding interest rate scheme, in detriment of the continuously compounding case often exploited in the literature.