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Master's Dissertation
DOI
10.11606/D.55.2002.tde-19062015-102731
Document
Author
Full name
Ulisses Umbelino dos Anjos
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2002
Supervisor
Committee
Andrade Filho, Marinho Gomes de (President)
Fragoso, Marcelo Dutra
Val, João Bosco Ribeiro do
Title in Portuguese
Inferência em processos de difusão com observações parciais e determinação da medida martingale equivalente na precificação de opções
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho foi feita uma aplicação das Equações Diferenciais Estocásticas á teoria da Precificação de Opções. Esta teoria teve grande impulso com o trabalho [Black & Scholes, 73], Black e Scholes em seu trabalho entre outra premissas feitas consideraram que os log-retornos dos ativos tinha uma distribuição normal. Aqui neste trabalho foram considerados três modelos, um deles é a difusão log- normal utilizada por Black-Scholes os outros dois modelos são a difusão linear e o processo de Ornstein-Uhlenbeck. Para estes três modelos foram determinadas as Medidas Martingales Equivalentes, isto foi feito utilizando o Teorema de Cameron-Martin- Girsanov, veja [Friedman, 75], Também foram analisadas versões discretas destes modelos obtidas pela aproximação de Euler, veja [Kloeden & Platen, 95]. O objetivo foi comparar os resultados obtidos com os modelos contínuos com os resultados obtidos com os modelos discretos. Também se fez uma análise dos estimadores dos parâmetros dos modelos contínuos. Nesta análise foi utilizada a abordagem Clássica e a abordagem Bayesiana. Primeiramente se fez uma comparação das estimativas obtidas por estas duas abordagens e posteriormente uma análise do comportamento assintótico desses estimadores.
Title in English
Inference in diffusion process with partial observations and the determining of the equivalent martingale measure in option pricing
Keywords in English
Not available
Abstract in English
In this work, an application of the stochastic differential equations to the theory of options was carried out. This theory had great impulse with the work by [Black & Scholes, 73], In their work, amongst other premi ses, they consider that the log-retums of actives had a normal distribution. In this work, three models were considered, one of which is the log-normal distribution used by Black & Scholes. The other two models are the linear diffusion and the Ornstein-Uhlenbeck. For these three models, the Equivalent Martingales Measures were determined, this was made using the theorem of Cameron-Martin-Girsanov, see [Friedman, 75], Discrete versions of these models were also analysed, which were obtained by the approximation of Euler, see [Kloeden & Platen, 95]. The objective was to compare the results for the continuous models to the results obtained for the discrete models. It was also made the analysis of the estimates of parameters of the continuous models. In this analysis, the Classic approach and the Bayesian approach were used. Firstly, a comparison was carried out for the estimates obtained for these two approaches and a further analysis of the asymptotic behaviour of these estimates was also made.
 
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UlissesUdosAnjos.pdf (2.73 Mbytes)
Publishing Date
2015-06-19
 
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