O mercado de opções de Petrobras é eficiente? Um estudo a partir da estratégia delta-gama-neutra

This study aims to verify if the Petrobras options market is efficient in the semi-strong form, that is, if all public information is reflected in these derivative prices. For this purpose, this work tries to achieve profit systematically through the Delta-GammaNeutral strategy using the company's stock and options. In order to simulate the strategy exactly as it would be used in the real world, we built the order books every five minutes considering all buying and selling orders sent to the underlying asset and to the options. We apply the strategy when distortions between implied volatilities extracted from the options are detected. The results show that the Petrobras options market is not efficient, since in 371 day trade strategies, which have an average investment of R$81,000 and average duration of one hour and thirteen minutes, the average return was 0.49% - which corresponds to more than 1,600% of the 1-day risk free interest rate - and 85% of strategies were profitable.

Volatilidade dos retornos e governança: um estudo de eventos da crise do subprime

The financial crisis that occurred between the years 2007 and 2008, known as the subprime crisis, has highlighted the governance of companies in Brazil and worldwide. To monitor the financial risk, quantitative tools of risk management were created in the 1990s, after several financial disasters. The market turmoil has also led companies to invest in the development and use of information, which are applied as tools to support process control and decision making. Numerous empirical studies on informational efficiency of the market have been made inside and outside Brazil, revealing whether the prices reflect the information available instantly. The creation of different levels of corporate governance on BOVESPA, in 2000, made the firms had greater impairment in relation to its shareholders with greater transparency in their information. The purpose of this study is to analyze how the subprime financial crisis has affected, between January 2007 and December 2009, the volatility of stock returns in the BM&BOVESPA of companies with greater liquidity at different levels of corporate governance. From studies of time series and through the studies of events, econometric tests were performed by the EVIEWS, and through the results obtained it became evident that the adoption of good practices of corporate governance affect the volatility of returns of companies

Volatilidade dos retornos e governança: um estudo de eventos da crise do subprime

The financial crisis that occurred between the years 2007 and 2008, known as the subprime crisis, has highlighted the governance of companies in Brazil and worldwide. To monitor the financial risk, quantitative tools of risk management were created in the 1990s, after several financial disasters. The market turmoil has also led companies to invest in the development and use of information, which are applied as tools to support process control and decision making. Numerous empirical studies on informational efficiency of the market have been made inside and outside Brazil, revealing whether the prices reflect the information available instantly. The creation of different levels of corporate governance on BOVESPA, in 2000, made the firms had greater impairment in relation to its shareholders with greater transparency in their information. The purpose of this study is to analyze how the subprime financial crisis has affected, between January 2007 and December 2009, the volatility of stock returns in the BM&BOVESPA of companies with greater liquidity at different levels of corporate governance. From studies of time series and through the studies of events, econometric tests were performed by the EVIEWS, and through the results obtained it became evident that the adoption of good practices of corporate governance affect the volatility of returns of companies

Volatilidade dos retornos e governança: um estudo de eventos da crise do subprime

The financial crisis that occurred between the years 2007 and 2008, known as the subprime crisis, has highlighted the governance of companies in Brazil and worldwide. To monitor the financial risk, quantitative tools of risk management were created in the 1990s, after several financial disasters. The market turmoil has also led companies to invest in the development and use of information, which are applied as tools to support process control and decision making. Numerous empirical studies on informational efficiency of the market have been made inside and outside Brazil, revealing whether the prices reflect the information available instantly. The creation of different levels of corporate governance on BOVESPA, in 2000, made the firms had greater impairment in relation to its shareholders with greater transparency in their information. The purpose of this study is to analyze how the subprime financial crisis has affected, between January 2007 and December 2009, the volatility of stock returns in the BM&BOVESPA of companies with greater liquidity at different levels of corporate governance. From studies of time series and through the studies of events, econometric tests were performed by the EVIEWS, and through the results obtained it became evident that the adoption of good practices of corporate governance affect the volatility of returns of companies

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

Mestrado em Contabilidade Internacional

On the goodness of fit of Kirk's formula for spread option prices

In this paper we investigate the goodness of fit of the Kirk's approximation formula for spread option prices in the correlated lognormal framework. Towards this end, we use the Malliavin calculus techniques to find an expression for the short-time implied volatility skew of options with random strikes. In particular, we obtain that this skew is very pronounced in the case of spread options with extremely high correlations, which cannot be reproduced by a constant volatility approximation as in the Kirk's formula. This fact agrees with the empirical evidence. Numerical examples are given.

Derivative hedging strategies for bitumen price risk

The objective of the study is to extend the existing hedging literature of the commodity price risks by investigating what kind of hedging strategies can be used in companies using bitumen as raw material in their production. Five different alternative swap hedging strategies in bitumen markets are empirically tested. Strategies tested are full hedge strategy, simple, conservative, and aggressive term structure strategies, and implied volatility strategy. The effectiveness of the alternative strategies is measured by excess returns compared to no hedge strategy. In addition, the downside risk of each strategy is measured with target absolute semi-deviation. Results indicate that any of the tested strategies does not outperform the no hedge strategy in terms of excess returns in all maturities. The best-performing aggressive term structure strategy succeeds to create positive excess returns only in short maturities. However, risk seems to increase hand-in-hand with the excess returns so that the best-performing strategies get the highest risk metrics as well. This implicates that the company willing to gain from favorable price movements must be ready to bear a greater risk. Thus, no superior hedging strategy over the others is found.

Asymmetric Smiles, Leverage Effects and Structural Parameters.

In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data.

Empirical Assessment of an Intertemporal Option Pricing Model with Latent variables

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility alone as in the Hull-White case. When we specialize this model to an equilibrium recursive utility model, we show through simulations that option prices are more informative than stock prices about the structural parameters of the model. We also show that a simple method of moments with a panel of option prices provides good estimates of the parameters of the model. This lays the ground for an empirical assessment of this equilibrium model with S&P 500 option prices in terms of pricing errors.

MA348exam 1998

Exam questions and solutions in LaTex

MA348exam 1998 pdf

Exam questions and solutions in PDF

Capturing UK real estate volitility

Volatility, or the variability of the underlying asset, is one of the key fundamental components of property derivative pricing and in the application of real option models in development analysis. There has been relatively little work on volatility in real terms of its application to property derivatives and the real options analysis. Most research on volatility stems from investment performance (Nathakumaran & Newell (1995), Brown & Matysiak 2000, Booth & Matysiak 2001). Historic standard deviation is often used as a proxy for volatility and there has been a reliance on indices, which are subject to valuation smoothing effects. Transaction prices are considered to be more volatile than the traditional standard deviations of appraisal based indices. This could lead, arguably, to inefficiencies and mis-pricing, particularly if it is also accepted that changes evolve randomly over time and where future volatility and not an ex-post measure is the key (Sing 1998). If history does not repeat, or provides an unreliable measure, then estimating model based (implied) volatility is an alternative approach (Patel & Sing 2000). This paper is the first of two that employ alternative approaches to calculating and capturing volatility in UK real estate for the purposes of applying the measure to derivative pricing and real option models. It draws on a uniquely constructed IPD/Gerald Eve transactions database, containing over 21,000 properties over the period 1983-2005. In this first paper the magnitude of historic amplification associated with asset returns by sector and geographic spread is looked at. In the subsequent paper the focus will be upon model based (implied) volatility.

The option market reaction to bank loan announcements

In this study, we examine the options market reaction to bank loan announcements for the population of US firms with traded options and loan announcements during 1996-2010. We get evidence on a significant options market reaction to bank loan announcements in terms of levels and changes in short-term implied volatility and its term structure, and observe significant decreases in short-term implied volatility, and significant increases in the slope of its term structure as a result of loan announcements. Our findings appear to be more pronounced for firms with more information asymmetry, lower credit ratings and loans with longer maturities and higher spreads. Evidence is consistent with loan announcements providing reassurance for investors in the short-term, however, over longer time horizons, the increase in the TSIV slope indicates that investors become increasingly unsure over the potential risks of loan repayment or uses of the proceeds.

Volatilidade implícita das opções de ações: uma análise sobre a volatilidade futura

O objetivo desse trabalho é avaliar a capacidade de previsão do mercado sobre a volatilidade futura a partir das informações obtidas nas opções de Petrobras e Vale, além de fazer uma comparação com modelos do tipo GARCH e EWMA. Estudos semelhantes foram realizados no mercado de ações americano: Seja com uma cesta de ações selecionadas ou com relação ao índice S&P 100, as conclusões foram diversas. Se Canina e Figlewski (1993) a “volatilidade implícita tem virtualmente nenhuma correlação com a volatilidade futura”, Christensen e Prabhala (1998) concluem que a volatilidade implícita é um bom preditor da volatilidade futura. No mercado brasileiro, Andrade e Tabak (2001) utilizam opções de dólar para estudar o conteúdo da informação no mercado de opções. Além disso, comparam o poder de previsão da volatilidade implícita com modelos de média móvel e do tipo GARCH. Os autores concluem que a volatilidade implícita é um estimador viesado da volatilidade futura mas de desempenho superior se comparada com modelos estatísticos. Gabe e Portugal (2003) comparam a volatilidade implícita das opções de Telemar (TNLP4) com modelos estatísticos do tipo GARCH. Nesse caso, volatilidade implícita tambem é um estimador viesado, mas os modelos estatísticos além de serem bons preditores, não apresentaram viés. Os dados desse trabalho foram obtidos ao longo de 2008 e início de 2009, optando-se por observações intradiárias das volatilidades implícitas das opções “no dinheiro” de Petrobrás e Vale dos dois primeiros vencimentos. A volatidade implícita observada no mercado para ambos os ativos contém informação relevante sobre a volatilidade futura, mas da mesma forma que em estudos anteriores, mostou-se viesada. No caso específico de Petrobrás, o modelo GARCH se mostrou um previsor eficiente da volatilidade futura