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Information Extraction of Probability and Risk of Returns using Options Prices
Cícha, Martin ; Trešl, Jiří (advisor) ; Cipra, Tomáš (referee) ; Málek, Jiří (referee)
The issue of forecasting the future price of risky financial assets has attracted academia and business practice since the inception of the stock exchange. Also due to the just finished financial crisis, which was the worst crisis since the Great Depression, it is clear that research in this area has not been finished yet. On the contrary, new challenges have been raised. The main goal of the thesis is the demonstration of the significant information potential which is hidden in option market prices. These prices contain informations on probability distribution of the underlying asset returns and the risk connected with these returns. Other objectives of the thesis are the forecast of the underlying asset price distribution using parametric and nonparametric estimates, the improvement of this forecast using the utility function of the representative investor, the description of the current market sentiment and the determination of the risk premium, especially the risk premium on Czech market. The thesis deals with the forecast of the underlying asset price probability distribution implied by the current option market prices using parametric and nonparametric estimates. The resulting distribution is described by the moment characteristics which represent a valuable tool for analyzing the current market sentiment. According to the theory, the probability distribution of the underlying asset price implied by option prices is risk neutral, i.e. it applies only to risk neutral investors. The theory further implies that the distribution of real world can be derived from the risk neutral distribution using utility function of the representative investor. The inclusion of a utility function of representative investor improves the forecast of the underlying asset price distribution. Three different utility functions of traditional risk theory are used in the thesis. These functions range from the simple power function to the general function of hyperbolic absolute risk aversion (HARA). Further, Friedman-Savage utility function is used. This function allows both a risk averse investor and a risk loving investor. The thesis also answers the question: Are the current asset prices at so high level that the purchase of the asset means a gamble? The risk premium associated with investing in the risky asset is derived in the thesis. The risk premium can be understood as the premium demanded by investors for investment in a risky asset against the investment in a riskless asset. All the theoretical methods introduced in the thesis are demonstrated on real data coming from two different markets. Developing market is represented by shares of CEZ and developed market is represented by S&P 500 futures. The thesis deals with demonstrations in single point in time as well as in available history of the data. The forecasts of the underlying asset price distribution and the relating risk premium are constructed in the available data history. The goals and the objectives of the thesis have been achieved. The contribution of the thesis is the development of parametric and nonparametric methodology for estimating the underlying asset price probability distribution implied by the option market prices so that the nature of the particular market and instrument is captured. The further contribution of the thesis is the construction of the forecasts of the underlying asset price distribution and the construction of the market sentiment in the available history of data. The contribution of the thesis is also the construction of the market risk premium in the available history and the establishment of the hypothesis that the markets gamble before the crisis.
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The study of the relationship between average realized stock returns and the risk of stock investment
Řípa, Daniel ; Bašta, Milan (advisor) ; Cícha, Martin (referee)
Bachelor thesis deals with the topic of average return rates of stock investments and assessment of their risk. The aim of this work is a comparison of two alternative approaches of risk measurement. Twenty years long time series of 30 stocks' returns from 1991 to 2010 are first used to analyze a relationship between average realized returns and standard deviations of the returns. Variety of computational algorithms is used in attempt to generalize this relationship. Analysis of the full length time series does not seem to discover a significant mutual relationship in the analyzed dataset. However, by analogically employing the algorithm of the CAPM analysis a significant and positive linear relationship between standard deviations and realized returns was found. Furthermore, two-step regression algorithm introduced by Fama & MacBeth is used to test the validity of CAPM model. This method led to the conclusion that CAPM cannot be rejected within the analyzed dataset. Moreover, strong positive linear relationship was found between the estimates of standard deviation and beta coefficients, which may be explained by the lack of variability in correlation between individual assets' and market portfolio's returns.
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