Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.5/3372
Título: Implied probability density functions: Estimation using hypergeometric, spline and lognormal functions
Autor: Santos, André Duarte dos
Orientador: Guerra, João
Data de Defesa: Mai-2011
Editora: Instituto Superior de Economia e Gestão
Citação: Santos, André Duarte dos. 2011. "Implied probability density functions: Estimation using hypergeometric, spline and lognormal functions". Dissertação de Mestrado. Universidade Técnica de Lisboa. Instituto Superior de Economia e Gestão
Resumo: This thesis examines the stability and accuracy of three different methods to estimate Risk-Neutral Density functions (RNDs) using European options. These methods are the Double-Lognormal Function (DLN), the Smoothed Implied Volatility Smile (SML) and the Density Functional Based on Confluent Hypergeometric function (DFCH). These methodologies were used to obtain the RNDs from the option prices with the underlying USDBRL (price of US dollars in terms of Brazilian reals) for different maturities (1, 3 and 6 months), and then tested in order to analyze which method best fits a simulated "true" world as estimated through the Heston model (accuracy measure) and which model has a better performance in terms of stability. We observed that in the majority of the cases the SML outperformed the DLN and DFCH in capturing the "true" implied skewness. The DFCH and DLN methods were better than the SML model at estimating the "true" Kurtosis. However, due to the higher sensitivity of the skewness and kurtosis measures to the tails of the distribution (all the information outside the available strike prices is extrapolated and the probability masses outside this range can have ininite forms) we also compared the tested models using the root mean integrated squared error (RMISE) which is less sensitive to the tails of the distribution. We observed that using the RMISE criteria, the DFCH outperformed the other methods as a better estimator of the "true" RND. Besides testing which model best captured the "true" world's expectations, we an¬alyzed the historical summary statistics of the RNDs obtained from the FX options on the USDBRL for the period between June 2006 (before the start of the subprime crisis) and February 2010 (seven months before the Brazilian general election).
Descrição: Master of Science in Finance
URI: http://hdl.handle.net/10400.5/3372
Aparece nas colecções:BISEG - Dissertações de Mestrado / Master Thesis
DG - Dissertações de Mestrado / Master Thesis

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