There has been an on-going debate about choices of the most suitable model amongst a variety of model specifications and parameterizations. The first dissertation essay investigates whether asymmetric leptokurtic return distributions such as Hansen's (1994) skewed tdistribution combined with GARCH specifications can outperform mixed GARCH-jump models such as Maheu and McCurdy's (2004) GARJI model incorporating the autoregressive conditional jump intensity parameterization in the discrete-time framework. I find that the more parsimonious GJR-HT model is superior to mixed GARCH-jump models. Likelihood-ratio (LR) tests, information criteria such as AIC, SC, and HQ and Value-at-Risk (VaR) analysis confirm that GJR-HT is one of the most suitable model specifications which gives us both better fit to the data and parsimony of parameterization. The benefits of estimating GARCH models using asymmetric leptokurtic distributions are more substantial for highly volatile series such as emerging stock markets, which have a higher degree of non-normality. Furthermore, Hansen's skewed t-distribution also provides us with an excellent risk management tool evidenced by VaR analysis. The second dissertation essay provides a variety of empirical evidences to support redundancy of stochastic volatility for SP500 index returns when stochastic volatility is taken into account with infinite activity pure Lévy jumps models and the importance of stochastic volatility to reduce pricing errors for SP500 index options without regard to jumps specifications. This finding is important because recent studies have shown that stochastic volatility in a continuous-time framework provides an excellent fit for financial asset returns when combined with finite-activity Merton's type compound Poisson jump-diffusion models. The second essay also shows that stochastic volatility with jumps (SVJ) and extended variance-gamma with stochastic volatility (EVGSV) models perform almost equally well for option pricing, which strongly imply that the type of Lévy jumps specifications is not important factors to enhance model performances once stochastic volatility is incorporated. In the second essay, I compute option prices via improved Fast Fourier Transform (FFT) algorithm using characteristic functions to match arbitrary log-strike grids with equal intervals with each moneyness and maturity of actual market option prices.

Submitted by RENATO MORI (rmori3@hotmail.com) on 2017-09-20T05:58:01Z No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2017-09-20T17:58:58Z (GMT) No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) / Made available in DSpace on 2017-09-21T13:36:32Z (GMT). No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) Previous issue date: 2017-08-22 / A proposta do estudo é aplicar ao Ibovespa, modelo paramétrico de VaR de 1 dia, com distribuição dos retornos dinâmica, que procura apreciar características empíricas comumente apresentadas por séries financeiras, como clusters de volatilidade e leptocurtose. O processo de retornos é modelado como um ARMA com erros GARCH que seguem distribuição t assimétrica. A metodologia foi comparada com o RiskMetrics e com modelos ARMA-GARCH com distribuição dos erros normal e t. Os modelos foram estimados diariamente usando uma janela móvel de 1008 dias. Foi verificado pelos backtests de Christoffersen e de Diebold, Gunther e Tay que dentre os modelos testados, o ARMA(2,2)- GARCH(2,1) com distribuição t assimétrica apresentou os melhores resultados. / The proposal of the study is to apply to Ibovespa a 1 day VaR parametric model, with dynamic distribution of returns, that aims to address empirical features usually seen in financial series, such as volatility clustering and leptocurtosis. The returns process is modeled as an ARMA with GARCH residuals that follow a skewed t distribution. The methodology was compared to RiskMetrics and to ARMA-GARCH with normal and t distributed residuals. The models were estimated every daily period using a window of 1008 days. By the backtests of Christoffersen and Diebold, Gunther and Tay, among the tested models, the ARMA(2,2)-GARCH(2,1) with skewed t distribution has given the best results.