Volatilidade implícita: Importância na valorização das opções financeiras e significado dos índices de volatilidade implícita

Mestrado em Contabilidade Internacional

Volatilidade implícita: estudo de caso

Mestrado em Controlo de Gestão dos Negócios

Opções reais: Avaliação do projecto de investimento de três parques eólicos em ambiente onshore e offshore

Os Projectos de Investimento desempenham um importante papel no crescimento económico-social dos países, proporcionando emprego e desenvolvimento tecnológico. Na óptica dos projectos inovadores, concretamente no sector das energias renováveis, acarretam elevados investimentos, numa base temporal de longo prazo. Nestes casos as decisões estratégicas assumem um papel determinante, assim, o principal objectivo desta dissertação é a utilização das Opções Reais como métrica de avaliação dos projectos de investimento. A análise e avaliação dos projectos implica em si incerteza nas previsões, desta forma, as Opções Reais minimizam o risco associado à incerteza através da inclusão da flexibilidade no processo de avaliação. A primeira parte da dissertação consiste na contextualização energética mundial e nacional, ao nível da energia primária e das energias renováveis, com incidência na energia eólica. A segunda consiste na introdução teórica dos projectos de investimento e dos conceitos inerentes às Opções Financeiras e às Opções Reais. Por último, apresenta-se um caso de estudo de construção de três parques eólicos e as consequentes decisões de investimento concluindo que os modelos de avaliação das Opções Reais proporcionam alternativas e interdependência em investimentos futuros.

Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

Is stock market volatility persistent? A fractionally integrated approach

This paper seeks to study the persistence in the G7’s stock market volatility, which is carried out using the GARCH, IGARCH and FIGARCH models. The data set consists of the daily returns of the S&P/TSX 60, CAC 40, DAX 30, MIB 30, NIKKEI 225, FTSE 100 and S&P 500 indexes over the period 1999-2009. The results evidences long memory in volatility, which is more pronounced in Germany, Italy and France. On the other hand, Japan appears as the country where this phenomenon is less obvious; nevertheless, the persistence prevails but with minor intensity.

Open and closed positions and stock index futures volatility

In this paper we analyze the relationship between volatility in index futures markets and the number of open and closed positions. We observe that, although in general both positions are positively correlated with contemporaneous volatility, in the case of S&P 500, only the number of open positions has influence over the volatility. Additionally, we observe a stronger positive relationship on days characterized by extreme movements of these contracting movements dominating the market. Finally, our findings suggest that day-traders are not associated to an increment of volatility, whereas uninformed traders, both opening and closing their positions, have to do with it.

The problem of estimating the volatility of zero coupon bond interest rate

Financial literature and financial industry use often zero coupon yield curves as input for testing hypotheses, pricing assets or managing risk. They assume this provided data as accurate. We analyse implications of the methodology and of the sample selection criteria used to estimate the zero coupon bond yield term structure on the resulting volatility of spot rates with different maturities. We obtain the volatility term structure using historical volatilities and Egarch volatilities. As input for these volatilities we consider our own spot rates estimation from GovPX bond data and three popular interest rates data sets: from the Federal Reserve Board, from the US Department of the Treasury (H15), and from Bloomberg. We find strong evidence that the resulting zero coupon bond yield volatility estimates as well as the correlation coefficients among spot and forward rates depend significantly on the data set. We observe relevant differences in economic terms when volatilities are used to price derivatives.

On the concept of endogenous volatility

Most financial and economic time-series display a strong volatility around their trends. The difficulty in explaining this volatility has led economists to interpret it as exogenous, i.e., as the result of forces that lie outside the scope of the assumed economic relations. Consequently, it becomes hard or impossible to formulate short-run forecasts on asset prices or on values of macroeconomic variables. However, many random looking economic and financial series may, in fact, be subject to deterministic irregular behavior, which can be measured and modelled. We address the notion of endogenous volatility and exemplify the concept with a simple business-cycles model.

Volatility regimes for the VIX index

This article presents a Markov chain framework to characterize the behavior of the CBOE Volatility Index (VIX index). Two possible regimes are considered: high volatility and low volatility. The specification accounts for deviations from normality and the existence of persistence in the evolution of the VIX index. Since the time evolution of the VIX index seems to indicate that its conditional variance is not constant over time, I consider two different versions of the model. In the first one, the variance of the index is a function of the volatility regime, whereas the second version includes an autoregressive conditional heteroskedasticity (ARCH) specification for the conditional variance of the index.

Industry concentration and market volatility

In this paper our aim is to gain a better understanding of the relationship between market volatility and industrial structure. As conflicting results have been documented regarding the relationship between market industry concentration and market volatility, this study investigates this relationship in the time series. We have found that this relationship is only significant and positive for Spain. Our results suggest that we cannot generalize across different countries that market industrial structure (concentration) is a significant factor in explaining market volatility.

Volatility forecasting with range models: An evaluation of new alternatives to the CARR model

The aim of this paper is to analyze the forecasting ability of the CARR model proposed by Chou (2005) using the S&P 500. We extend the data sample, allowing for the analysis of different stock market circumstances and propose the use of various range estimators in order to analyze their forecasting performance. Our results show that there are two range-based models that outperform the forecasting ability of the GARCH model. The Parkinson model is better for upward trends and volatilities which are higher and lower than the mean while the CARR model is better for downward trends and mean volatilities.