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Master's Dissertation
DOI
10.11606/D.12.2003.tde-10062007-134238
Document
Author
Full name
Ruy Gabriel Balieiro Filho
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2003
Supervisor
Committee
Rosenfeld, Rogério (President)
Athayde, Gustavo Monteiro de
Silva, Marcos Eugenio da
Title in Portuguese
Aplicações da expansão de Edgeworth à precificação de derivativos financeiros
Keywords in Portuguese
Assimetria
Black-Scholes
Curtose
Edgeworth
Hedge
Não-normalidade
Opções
Smile
Abstract in Portuguese
O Objetivo deste trabalho é usar uma ferramenta matemática conhecida como expansão de Edgeworth em conjunto com a moderna teoria de análise de derivativos financeiros que utilizam o método de precificação neutra ao risco. Tal expansão permite obter uma função densidade de probabilidade com assimetria e curtose arbitrárias a partir de uma densidade normal. Desta forma, podemos usar esta nova distribuição como a state price density do ativo-objeto procurando corrigir o sorriso da volatilidade através da definição de funções de probabilidade com assimetrias positivas ou negativas e curtose maior de que três. Além disso esperamos também chegar a uma nova maneira de realizar o delta hedge de uma carteira de replicação de modo mais eficiente do que a de Black-Scholes.
Title in English
Testing option pricing with the Edgeworth expansion
Keywords in English
Black-Scholes
Edgeworth
Kurtosis
Options
Skewness
Abstract in English
There is a well-developed framework, the Black?Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is 2awed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black?Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more e6cient hedging strategies of these instruments.
 
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tesefinal_Edgeworth.pdf (303.43 Kbytes)
Publishing Date
2007-06-15
 
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