DOI
https://doi.org/10.11606/T.12.2005.tde-14122022-095219
Documento
Autor
Nome completo
Thierry Barbe
E-mail
Área do Conhecimento
Data de Defesa
Imprenta
São Paulo, 2005
Silva, Marcos Eugenio da (Presidente)
Costa, Oswaldo Luiz do Valle
Rosenfeld, Rogério
Santos, Jose Carlos de Souza
Siqueira, Jose de Oliveira
Título em português
Um novo algoritmo para aplicações das seqüências de Sobol à precificação de derivativos financeiros
Palavras-chave em português
Derivativos
Finanças
Método de Monte Carlo
Resumo em português
Título em inglês
A new algorithm for applying Sobol sequences to the pricing of financial derivatives
Palavras-chave em inglês
Derivatives
Finance
Monte Carlo Method
Resumo em inglês
During the latter half of the twentieth century Monte Carlo gained enormous popularity, both for its efficiency and ease of implementation. However, its use requires great computational cost, a factor that has limited its expansion. This is why a great deal of effort has been spent in an effort to discover ways to reduce this burden. Variance reduction techniques are an example of this line of research. Another technique that seeks faster convergence consists in picking beforehand the randomnumbers used in the simulation. When these numbers are chosen from low discrepancy sequences the method is then called quasi Monte Carlo and has proved more efficient than traditional Monte Carlo for solving a vast array of problems. Nonetheless, its use has been confined to simulations in low dimensional spaces, for, like other deterministic methods, it suflfers from the curse of dimensionality. Researchers are now challenged to extend the use of quasi Monte Carlo to problems of very high dimension. Various Solutions have been suggested but none has managed to deal with problems of very high dimensions. Furthermore, it has been shown that in various cases where satisfactory results we reached for médium to high dimensional problems the simulation was in fact sensitive only to a subset of much lower dimension. This generated the distinction between nominal and effective dimension of the Monte Carlo simulation. Our work presents a method that unleashes the use of Sobol sequences to dimensions much higher than those for which it has insofar proved operational. This goes through the discovery of a uniformity property implicit in the directional numbers and the implementation of an algorithm that generates efficient directional numbers. The construction is then tested in different settings which range from the estimation of test integrals to the pricing of instruments that belong to three different families of financial derivatives. For the first time in the quasi Monte Carlo literature in finance the analysis takes into consideration the dichotomy between nominal and effective dimension thus reducing much of the bias present in previous tests. Excellent results were obtained for simulations with effective dimension ranging up to 2000.

AVISO - A consulta a este documento fica condicionada na aceitação das seguintes condições de uso:
Este trabalho é somente para uso privado de atividades de pesquisa e ensino. Não é autorizada sua reprodução para quaisquer fins lucrativos. Esta reserva de direitos abrange a todos os dados do documento bem como seu conteúdo. Na utilização ou citação de partes do documento é obrigatório mencionar nome da pessoa autora do trabalho.
DrThierryBarbe.pdf (2.04 Mbytes)
Data de Publicação
2022-12-14

AVISO: Saiba o que são os trabalhos decorrentes clicando aqui.
Todos os direitos da tese/dissertação são de seus autores
CeTI-SC/STI