<p>Due to the advancements in computing power and the availability of high-frequency data, the analyses of the high frequency stock data and market microstructure has become more and more important in econometrics. In the high frequency data setting, volatility is a very important indicator on the movement of stock prices and measure of risk. It is a key input in pricing of assets, portfolio reallocation, and risk management. In this thesis, we use the Heterogeneous Autoregressive model of realized volatility, combined with Bayesian inference as well as Markov chain Monte Carlo method’s to estimate the innovation density of the daily realized volatility. A Dirichlet process is used as the prior in a countably infinite mixture model. The semi-parametric model provides a robust alternative to the models used in the literature. I find evidence of thick tails in the density of innovations to log-realized volatility.</p> / Master of Science (MSc)

Submitted by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-06-18T18:53:22Z No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) / Approved for entry into archive by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-06-18T18:54:14Z (GMT) No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) / Made available in DSpace on 2018-06-18T18:54:14Z (GMT). No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) Previous issue date: 2018-02-27 / Given the importance of market risk measures, such as value at risk (VaR), in this paper, we compare traditionally accepted volatility forecast models, in particular, the GARCH family models, with more recent models such as HAR-RV and GAS in terms of the accuracy of their VaR forecasts. For this purpose, we use intraday prices, at the 5-minute frequency, of the S&P 500 index and the General Electric stocks, for the period from January 4, 2010 to December 30, 2013. Based on the tick loss function and the Diebold-Mariano test, we did not find difference in the predictive performance of the HAR-RV and GAS models in comparison with the Exponential GARCH (EGARCH) model, considering daily VaR forecasts at the 1% and 5% significance levels for the return series of the S&P 500 index. Regarding the return series of General Electric, the 1% VaR forecasts obtained from the HAR-RV models, assuming a t-Student distribution for the daily returns, are more accurate than the forecasts of the EGARCH model. In the case of the 5% VaR forecasts, all variations of the HAR-RV model perform better than the EGARCH. Our empirical study provides evidence of the good performance of HAR-RV models in forecasting value at risk. / Dada a importância de medidas de risco de mercado, como o valor em risco (VaR), nesse trabalho, comparamos modelos de previsão de volatilidade tradicionalmente mais aceitos, em particular, os modelos da família GARCH, com modelos mais recentes, como o HAR-RV e o GAS, em termos da acurácia de suas previsões de VaR. Para isso, usamos preços intradiários, na frequência de 5 minutos, do índice S&P 500 e das ações da General Electric, para o período de 4 de janeiro de 2010 a 30 de dezembro de 2013. Com base na função perda tick e no teste de Diebold-Mariano, não encontramos diferença no desempenho preditivo dos modelos HAR-RV e GAS em relação ao modelo Exponential GARCH (EGARCH), considerando as previsões de VaR diário a 1% e 5% de significância para a série de retornos do índice S&P 500. Já com relação à série de retornos da General Electric, as previsões de VaR a 1% obtidas a partir dos modelos HAR-RV, assumindo uma distribuição t-Student para os retornos diários, mostram-se mais acuradas do que as previsões do modelo EGARCH. No caso das previsões de VaR a 5%, todas as variações do modelo HAR-RV apresentam desempenho superior ao EGARCH. Nosso estudo empírico traz evidências do bom desempenho dos modelos HAR-RV na previsão de valor em risco.

近年來，金融資產報酬波動的推估一直是重要的研究課題。然而，過去的波動不對稱研究均集中在股票市場，探討外匯市場波動不對稱性的實證研究並不多，但若忽略其不對稱效果將影響未來波動預測的正確性。因此，本研究利用近十六年來美元及日圓兌台幣匯率日資料，以傳統的波動不對稱性指數型GARCH模型(EGARCH Model)、門檻型GARCH模型(TGARCH, GJR GARCH Model)，亦延用異質自我相關迴歸模型(HAR-RV Model)及修正型異質自我相關迴歸模型(Modified HAR-RV Model)分別探討美元及日圓兌台幣匯率波動是否存在不對稱現象及其不對稱程度，並加以分析。實證研究中，上述四種模型均顯示美元及日圓兌台幣匯率波動的確具有不對稱效果；美元兌台幣匯率波動，與股票市場一致，報酬率與波動度間呈負向關係，當台幣相對美元升值時，波動度較高；而日圓兌台幣匯率波動，與美元匯率變動方向相反，報酬率與波動度間呈正向關係，當台幣相對日圓貶值時，波動度較高。此外，以異質自我相關迴歸模型實證分析中，日波動落後項的影響力明顯大於週、月、季波動落後項，與Muller, et al. (1997)、Corsi (2004)及Andersen, et al. (2005)實證研究結果類似。