The informational content of implied volatility and its prediction power is evaluated for time horizons of one month. The study covers the period of November 2007 to November 2013 for the two indices S&P500 and OMXS30. The findings are put in relation to the corresponding results for past realized volatility. We find results supporting that implied volatility is an efficient, although biased estimator of realized volatility. Our results support the common notion that implied volatility predicts realized volatility better than past realized volatility, and that it also subsumes most of the informational content of past realized volatility.

Under a class of one dimensional local volatility models, this thesis establishes closed form small time asymptotic formulae for the gradient of the implied volatility, whether or not the options are at the money, and for the at the money Hessian of the implied volatility. Along the way it also partially verifies the statement by Berestycki, Busca and Florent (2004) that the implied volatility admits higher order Taylor series expansions in time near expiry. Both as a prelude to the presentation of these main results and as a highlight of the importance of the no arbitrage condition, this thesis shows in its beginning a Cox-Ingersoll-Ross type stock model where an equivalent martingale measure does not always exist.

Over the past couple of decades, the number of volatility indices has increased rapidly. These indices seek to represent the market’s expectation of realized volatility over the coming month, based on the prices of options traded on each underlying equity index. Although the dynamics of realized volatility spillover have been studied extensively, very few studies exists that examine the spillover between these volatility indices. By using DAG-based structural vector autoregression, this paper provides evidence that implied volatility spillover differs from realized volatility spillover. Through solving the well-known VAR identification problem for these indices, this paper finds that Asia, more specifically Hong Kong, plays a central role in implied volatility spillover during and after the 2008 financial crisis.

This study tests if historical volatility- and implied volatility has significant predictive power over future realized volatility and if so which one of the two is the superior predictor. The study is conducted by using historical volatility of the OMXS30 and implied volatility from OMXS30 call options during the period 2012-2023. Three regressions have been made to test the research questions, two simple linear regression and one multiple linear regression. The results of the study showed that both historical- and implied volatility had significant predictive power over future realized volatility with implied being the superior one with a higher correlation coefficient. The multiple regression showed that both the independent variables were important and both of them explained different parts of the data, which means that they have complementary abilities and that both should be used when assessing the forecast of realized volatility.

In this thesis, we derive a closed-form approximation to the implied volatility for a European option, assuming that the underlying asset follows the generalized Heston model. A new para- meter is added to the Heston model which constructed the generalized Heston model. Based on the results in Lorig, Pagliarani and Pascucci [11], we obtain implied volatility expansions up to third-order. We conduct numerical studies to check the accuracy of our expansions. More specifically we compare the implied volatilities computed using our expansions to the results by Monte Carlo simulation method. Our numerical results show that the third-order implied volatility expansion provides a very good approximation to the true value.

[pt] O presente trabalho busca explorar a previsibilidade na dinâmica temporal em modelos lineares de superfícies de volatilidade implícita estimados para opções de compra de ações brasileiras. Resultados de estudos anteriores, sob a abordagem usualmente empregada de estimação de modelos lineares em função do preço de exercício e do tempo até o vencimento a partir de dados de corte transversal sobre cada contrato disponível em dado instante, como Dumas, Fleming e Whaley (1998), revelam grande instabilidade nos coeficientes estimados ao longo do tempo. Por conseguinte, a incapacidade desta perspectiva em descrever a dinâmica intertemporal da estrutura, contrariando a observação empírica de volatilidade variável no tempo. A partir destas evidências e das conclusões de Heston e Nandi (2000), que reportaram significativa dependência da trajetória para a volatilidade dos retornos do índice S&P 500, Gonçalves e Guidolim (2006), propuseram um modelo em dois estágios, que aplica vetores autoregressivos para capturar a presença de variação temporal dos coeficientes de um modelo linear. A contribuição deste trabalho está em aplicar o Modelo proposto à realidade do mercado brasileiro de opções de ações, incipiente em liquidez e horizonte de negociação se comparado ao mercado norte americano, adaptando critérios a fim de validar sua aplicabilidade neste contexto em termos estatísticos e econômicos. Os resultados comprovam a superioridade desta abordagem em relação a outras comparáveis na literatura, mas não a capacidade de gerar retornos acima da média na presença de custos de transação contra a referência natural da taxa livre de risco. O que sugere a adequação à hipótese de eficiência de mercado. / [en] O The present study aims to explore predictability in temporal dynamics regarding linear models of the implied volatility surfaces estimated for Brazilian stocks options. Previous results, by usual approach of fitting linear models linking implied volatility to time to maturity and moneyness, available for each cross-section of option contracts at a point in time, as in Dumas, Fleming and Whaley (1998), suggest that estimated parameters of such models are highly unstable over time. Therefore, this approach isn t capable of replicating various IVS s shapes, contrary to the empirical evidence of implied volatility varying with options strike price and date of expiration. Based on these evidences and in Heston and Nandi (2000), that exploit the information on path-dependency in volatility contained in the spot S&P 500 index, Gonçalves e Guidolim (2006) proposed a two-stage approach to modeling and forecasting the S&P 500 index options IVS. In the second-stage they model the dynamics of the cross-sectional first-stage coefficients by means of vector autoregression models. The contribution of this work is to apply the proposed model to the reality of the Brazilian stock options, incipient in terms of liquidity and trading horizon dimensions when compared to the U.S. market, adapting criterians to validate its applicability in this context in statistical and economical sense. The results demonstrate the superiority of this approach over comparable literature, but not the ability to generate abnormal profits in the presence of transaction costs in excess of the benchmark of the risk-free rate. This indicates adaptation to the market efficiency hypothesis.

Master of Science / Department of Agricultural Economics / Glynn Tonsor / This decade has seen movements in commodity futures markets never seen before. There are many factors that have intensified price movements and volatility behavior. Those factors likely altering supply and demand include governmental policy within and outside of the U.S, weather shocks, geopolitical conflicts, food safety concerns etc. Whatever the reasons are for price movements it is clear that the volatility behavior in commodity markets constantly change, and risk managers need to use current and efficient tools to mitigate price risk. This study identified market structural breaks of realized volatility in corn, wheat, soybeans, live cattle, feeder cattle and lean hogs futures markets. Furthermore, this study analyzes the forecasting performance of implied volatility, historical volatility, a composite approach and a naïve approach as forecasters of realized volatility. The forecasting performance of these methods was analyzed in the full period of time of our weekly data from January 1995 to April 2014 and in each identified market regime for each commodity. Previous research has analyzed forecasting performance of implied volatility, a time series alternative and a composite method. However, to the best of my knowledge, they have not worried about market structural breaks in the data that might influence the performance of the mentioned forecasting methods in different periods of time. Overall, results indicate that indeed there are multiple market structural breaks present in the volatility datasets across all six commodities. We found differences in the forecasting performance of the analyzed methods when individual market regimes were analyzed. There seems to be evidence that corroborates the idea in the literature about the superiority of implied volatility over a historical volatility, a composite approach and a naïve approach. Additionally, implied volatility encompassed all the information contained in the historical volatility and the naïve measure across each identified market regime in all six commodities. Our results show that when both implied volatility and historical volatility are available, the benefit of combining those measures into a composite forecasting approach is very limited. Our results hold true for a short term 1 week ahead realized volatility forecast. It would be of interest to see how results vary for longer forecasting time horizons.

This thesis will investigate if adding an exogenous variable (implied volatility) to the variance equation will increase the performance for the GARCH(1,1) and EGARCH(1,1) models based on the OMXS30 index. These models are also compared with the implied volatility itself as a forecasting/modeling method. To evaluate the models the realized variance will be used as an unbiased estimator of the conditional variance. The findings suggest that adding implied volatility to the variance equation increase the overall performance.

Chapter 1 of the dissertation investigates the firms' restructuring choice between minority carve-outs and tracking stocks using samples during 1990-2001. The extra compensation from the restructured units, the liquidity conditions, and the preservation of synergy are the significant factors determining a firm's restructuring decision. Additional compensation seems to be a major driving force behind restructuring via tracking stock. One year after the restructuring, the executive compensation of the tracking stock group increases by 241% compared to 32% for the carve-out sample. In spite of the significant increase in the compensation, the three-year buy-and-hold return for tracking stock parents is more negative than that of the carve-out parents. Thus, if the extra compensation was designed to align the interests of managers and shareholders, the goal did not materialize. The primary motive behind restructuring through carve-outs is to control the liquidity problem. Although the operating performance of the parents of either group does not improve three years after the restructuring, the long-term stock performance of carve-out parents improves when a restructured unit is less related to the parent. Chapter 2 of the dissertation compares the degree of overreaction between value stocks and growth stocks using the implied volatility from option prices. Applying Stein's (1989) mean reversion model and Heynen, Kemna, and Vorst's (1994) GARCH and EGARCH methods, I compare the theoretical and empirical measures of reaction of longterm options in respect to short-term options for the growth and the value portfolios, which are separately classified by price-to-book and price-to-earning ratios. The evidence suggests that growth portfolios largely overreact to a greater degree than the value portfolios assuming mean reversion, GARCH, and EGARCH models. The findings potentially explain why value stocks outperform growth stocks in the long run, lending support to overreaction as an explanation for the value effect.

[pt] A expansão do mercado de derivativos no mundo e principalmente no Brasil tem impulsionado seus usuários a aprimorar e desenvolver ferramentas de apreçamento mais eficientes. Com esse intuito, o presente trabalho tem por objetivo evidenciar qual janela de observações gera a curtose e a assimetria que mais suavize o sorriso da volatilidade utilizando-se do modelo Corrado-Su. Para tanto, as empresas escolhidas foram a Petrobrás PN e a Vale PNA, devido a suas ações e opções de compra serem as mais líquidas no mercado brasileiro. A análise dos dados apontou para uma maior suavização do sorriso da volatilidade por parte das janelas de dados de curto prazo sobre as longo prazo, e uma equivalência de desempenho das primeiras ao do modelo Black-Scholes. / [en] The expansion of the derivatives market in the world and especially in Brazil has driven its users to enhance and develop tools for more efficient pricing. With this purpose, this paper aims to point which window of observations generates the kurtosis and skewness that more soften the volatility smile using the Corrado-Su model. Therefore, the firms that were chosen were Petrobras PN and Vale PNA, because their stocks and options are the most liquid in Brazilian market. The data analysis indicated a greater smoothing volatility smile using the windows of observations of the short term instead of the long term, and a equivalent performance of the first ones to that of the Black-Scholes model.