22 resultados para implied trees
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Abstract
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The paper studies the relationship between implied volatility and realized volatility by utilizing regression analysis and correlations.
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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.
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The purpose of this thesis is to investigate scheduled market announcements’ effects on Euro implied volatility. Timeline selected for this study ranges from 2005 to 2009. The method chosen is so-called event study approach, in which five days prior to a news announcement stand for a pre-event period, and five days after the announcement form a post-event period. Statistical research method employed is Mann-Whitney-Wilcoxon test, which examines two evenly-sized distributions’ equality, in this case the distributions being the pre- and post-event periods. Observations are based on daily data of US dollar nominated Euro at-the-money call options. Research results partially back up previous literature’s view of uncertainty increasing prior to the news announcement. After the exact contents of the news is public, uncertainty levels measured by implied volatility tend to lower.
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Volatility has a central role in various theoretical and practical applications in financial markets. These include the applications related to portfolio theory, derivatives pricing and financial risk management. Both theoretical and practical applications require good estimates and forecasts for the asset return volatility. The goal of this study is to examine the forecast performance of one of the more recent volatility measures, model-free implied volatility. Model-free implied volatility is extracted from the prices in the option markets, and it aims to provide an unbiased estimate for the market’s expectation on the future level of volatility. Since it is extracted from the option prices, model-free implied volatility should contain all the relevant information that the market participants have. Moreover, model-free implied volatility requires less restrictive assumptions than the commonly used Black-Scholes implied volatility, which means that it should be less biased estimate for the market’s expectations. Therefore, it should also be a better forecast for the future volatility. The forecast performance of model-free implied volatility is evaluated by comparing it to the forecast performance of Black-Scholes implied volatility and GARCH(1,1) forecast. Weekly forecasts for six years period were calculated for the forecasted variable, German stock market index DAX. The data consisted of price observations for DAX index options. The forecast performance was measured using econometric methods, which aimed to capture the biasedness, accuracy and the information content of the forecasts. The results of the study suggest that the forecast performance of model-free implied volatility is superior to forecast performance of GARCH(1,1) forecast. However, the results also suggest that the forecast performance of model-free implied volatility is not as good as the forecast performance of Black-Scholes implied volatility, which is against the hypotheses based on theory. The results of this study are consistent with the majority of prior research on the subject.