Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts

Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors' risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main ndings are as follows. First, we con rm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

Overconfidence and market efficiency with heterogeneous agents

We study financial markets in which both rational and overconfident agents coexist and make endogenous information acquisition decisions. We demonstrate the following irrelevance result: when a positive fraction of rational agents (endogeneously) decides to become informed in equilibrium, prices are set as if all investors were rational, and as a consequence the overconfidence bias does not aect informational efficiency, price volatility, rational traders expected profits or their welfare. Intuitively, as overconfidence goes up, so does price infornativeness, which makes rational agents cut their information acquisition activities, effectively undoing the standard effect of more aggressive trading by the overconfident.

VIX as a stock market indicator

The goal of this research was to make an overall sight to VIX and how it can be used as a stock market indicator. Volatility index, often referred as the fear index, measures how much does it cost for investor to protect his/hers S&P 500 position from fluctuations with options. Over the relatively short history of VIX it has succesfull timing coordinator and it has told about the market state adding its own psychological view of the amount of fear and greed.

Is it possible to utilize VIX for a profitable trading strategy of S&P 500 Index?

The goal of this research was to make an overall sight to VIX® and how it can be used as a stock market indicator. Volatility index often referred as the fear index, measures how much it costs for investor to protect his/her S&P 500 position from fluctuations with options. Over the relatively short history of VIX it has been a successful timing coordinator and it has given incremental information about the market state adding its own psychological view of the amount of fear and greed. Correctly utilized VIX information gives a considerable advantage in timing market actions. In this paper we test how VIX works as a leading indicator of broad stock market index such as S&P 500 (SPX). The purpose of this paper is to find a working way to interpret VIX. The various tests are made on time series data ranging from the year 1990 to the year 2010. The 10-day simple moving average strategy gave significant profits from the whole time when VIX data is available. Strategy was able to utilize the increases of SPX in example portfolio value and was able to step aside when SPX was declining. At the times when portfolio was aside of S it was on safety fund like on treasury bills getting an annual yield of 3 percent. On the other side just a static number’s of VIX did not work as indicators in a profit making way.

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.

Hedging options in a garch environment: testing the term structure of stochastic volatility models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P500 index volatility. U sing measurements of the ability of volatility models to hedge and value term structure dependent option positions, we fmd that hedging tests support the Black-Scholes delta and gamma hedges, but not the simple vega hedge when there is no model of the term structure of volatility. With various models, it is difficult to improve on a simple gamma hedge assuming constant volatility. Ofthe volatility models, the GARCH components estimate of term structure is preferred. Valuation tests indicate that all the models contain term structure information not incorporated in market prices.

Volatilidade implícita: estudo de caso

Mestrado em Controlo de Gestão dos Negócios

Trade disclosure and price dispersion

This paper determines the effects of post-trade opaqueness on market performance. We find that the degree of market transparency has important effects on market equilibria. In particular, we show that dealers operating in a transparent structure set regret-free prices at each period making zero expected profits in each of the two trading rounds, whereas in the opaque market dealers invest in acquiring information at the beginning of the trading day. Moreover, we obtain that if there is no trading activity in the first period, then market makers only change their quotes in the opaque market. Additionally, we show that trade disclosure increases the informational efficiency of transaction prices and reduces volatility. Finally, concerning welfare of market participants, we obtain ambiguous results. Keywords: Market microstructure, Post-trade transparency, Price experimentation, Price dispersion.

On Option Price Information Content and Extraction of Implied Probability Distributions

In this study we used market settlement prices of European call options on stock index futures to extract implied probability distribution function (PDF). The method used produces a PDF of returns of an underlying asset at expiration date from implied volatility smile. With this method, the assumption of lognormal distribution (Black-Scholes model) is tested. The market view of the asset price dynamics can then be used for various purposes (hedging, speculation). We used the so called smoothing approach for implied PDF extraction presented by Shimko (1993). In our analysis we obtained implied volatility smiles from index futures markets (S&P 500 and DAX indices) and standardized them. The method introduced by Breeden and Litzenberger (1978) was then used on PDF extraction. The results show significant deviations from the assumption of lognormal returns for S&P500 options while DAX options mostly fit the lognormal distribution. A deviant subjective view of PDF can be used to form a strategy as discussed in the last section.

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

Previsão de volatilidade: uma comparação entre volatilidade implícita e realizada

Com origem no setor imobiliário americano, a crise de crédito de 2008 gerou grandes perdas nos mercados ao redor do mundo. O mês de outubro do mesmo ano concentrou a maior parte da turbulência, apresentando também uma explosão na volatilidade. Em meados de 2006 e 2007, o VIX, um índice de volatilidade implícita das opções do S&P500, registrou uma elevação de patamar, sinalizando o possível desequilíbrio existente no mercado americano. Esta dissertação analisa se o consenso de que a volatilidade implícita é a melhor previsora da volatilidade futura permanece durante o período de crise. Os resultados indicam que o VIX perde poder explicativo ao se passar do período sem crise para o de crise, sendo ultrapassado pela volatilidade realizada.

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

Este trabalho tem como objetivo verificar se o mercado de opções da Petrobras PN (PETR4) é ineficiente na forma fraca, ou seja, se as informações públicas estão ou não refletidas nos preços dos ativos. Para isso, tenta-se obter lucro sistemático por meio da estratégia Delta-Gama-Neutra que utiliza a ação preferencial e as opções de compra da empresa. Essa ação foi escolhida, uma vez que as suas opções tinham alto grau de liquidez durante todo o período estudado (01/10/2012 a 31/03/2013). Para a realização do estudo, foram consideradas as ordens de compra e venda enviadas tanto para o ativo-objeto quanto para as opções de forma a chegar ao livro de ofertas (book) real de todos os instrumentos a cada cinco minutos. A estratégia foi utilizada quando distorções entre a Volatilidade Implícita, calculada pelo modelo Black & Scholes, e a volatilidade calculada por alisamento exponencial (EWMA – Exponentially Weighted Moving Average) foram observadas. Os resultados obtidos mostraram que o mercado de opções de Petrobras não é eficiente em sua forma fraca, já que em 371 operações realizadas durante esse período, 85% delas foram lucrativas, com resultado médio de 0,49% e o tempo médio de duração de cada operação sendo pouco menor que uma hora e treze minutos.