<p>Condfidence in the future is a signicant factor for business development. However frequently, accurate and specific purposes are spread over the market environment influence.Thus,it is necessary to make an appropriate consideration of instability, which is peculiar to the dynamic development. Volatility, variance and standard deviation are used to</p><p>characterize the deviation of the investigated quantity from mean value.</p><p>Volatility is one of the main instruments to measure the risk of the asset.</p><p>The increasing availability of financial market data has enlarged volatility research potential but has also encouraged research into longer horizon volatility forecasts.</p><p>In this paper we investigate stock index volatility with respect to capitalization with help of GARCH-modelling.</p><p>There are chosen three indexes of OMX Nordic Exchange for our research. The Nordic list segment indexes comprising Nordic Large Cap,</p><p>Mid Cap and Small Cap are based on the three market capitalization groups.</p><p>We implement GARCH-modeling for considering indexes and compare our results in order to conclude which ones of the indexes is more volatile.</p><p>The OMX Nordic list indexis quiet new(2002)and reorganized as late as October 2006. The current value is now about 300 and no options do exist. In current work we are also interested in estimation of the Heston</p><p>model(SVmodel), which is popular in financial world and can be used in option pricing in the future.</p><p>The results of our investigations show that Large Cap Index is more volatile then Middle and Small Cap Indexes.</p>

<p>The famous Black-Scholes (BS) model used in the option pricing theory</p><p>contains two parameters - a volatility and an interest rate. Both</p><p>parameters should be determined before the price evaluation procedure</p><p>starts. Usually one use the historical data to guess the value of these</p><p>parameters. For short lifetime options the interest rate can be estimated</p><p>in proper way, but the volatility estimation is, as well in this case,</p><p>more demanding. It turns out that the volatility should be considered</p><p>as a function of the asset prices and time to make the valuation self</p><p>consistent. One of the approaches to this problem is the method of</p><p>uncertain volatility and the static hedging. In this case the envelopes</p><p>for the maximal and minimal estimated option price will be introduced.</p><p>The envelopes will be described by the Black - Scholes - Barenblatt</p><p>(BSB) equations. The existence of the upper and lower bounds for the</p><p>option price makes it possible to develop the worse and the best cases</p><p>scenario for the given portfolio. These estimations will be financially</p><p>relevant if the upper and lower envelopes lie relatively narrow to each</p><p>other. One of the ideas to converge envelopes to an unknown solution</p><p>is the possibility to introduce an optimal static hedged portfolio.</p>

<p>In this paper we investigate pricing of variance swaps contracts. The</p><p>literature is mostly dedicated to the pricing using replication with</p><p>portfolio of vanilla options. In some papers the valuation with stochastic</p><p>volatility models is discussed as well. Stochastic volatility is becoming</p><p>more and more interesting to the investors. Therefore we decided to</p><p>perform valuation with the Heston stochastic volatility model, as well</p><p>as by using replication strategy.</p><p>The thesis was done at SunGard Front Arena, so for testing the replica-</p><p>tion strategy Front Arena software was used. For calibration and testing</p><p>of the Heston model we used MatLab.</p>

This dissertation examines stock return predictability with aggregate credit conditions. The aggregate credit conditions are empirically measured by credit standards (Standards) derived from the Federal Reserve Board's Senior Loan Officer Opinion Survey on Bank Lending Practices. Using Standards, this study investigates whether the aggregate credit conditions predict the expected returns and volatility of the stock market. The first essay, "Credit Conditions and Expected Stock Returns," analyzes the predictability of U.S. aggregate stock returns using a measure of credit conditions, Standards. The analysis reveals that Standards is a strong predictor of stock returns at a business cycle frequency, especially in the post-1990 data period. Empirically the essay demonstrates that a tightening of Standards predicts lower future stock returns. Standards performs well both in-sample and out-of-sample and is robust to a host of consistency checks including a small sample analysis. The second essay, "Credit Conditions and Stock Return Volatility," examines the role played by credit conditions in predicting aggregate stock market return volatility. The essay employs a measure of credit conditions, Standards in the stock return volatility prediction. Using the level and the log of realized volatility as the estimator of the stock return volatility, this study finds that Standards is a strong predictor of U.S. stock return volatility. Overall, the forecasting power of Standards is strongest during tightening credit periods.

The volatility of share prices is an important variable in most asset pricing models and option pricing formulas.Valuation of volatility of share prices have become a major challenge with the development of the knowledge-driven economy as evidence suggest that not all elements of company wealth are physical in nature. The purpose of this project entitled “The intensity of the firm’s intangible asset on the volatility of their stock price” is to check if the intensity of intangible assets in a firm’s balance sheet affects the volatility of their stock price. A brief overview of intangible assets is also included in this study. An OLS regression was run and the results of the entire data set gives a negative correlation between intensity of intangible assets and volatility of stock prices probably due to the fact that the volatility of the firm share prices are driven by uncertainty and expectation of future growth. An industry-grouping regression was carried out, the results shows that for basic pharmaceuticals there is a positive correlation between the intensity of intangible assets and their price volatility while the other three industry groups produce a negative correlation. The study relies on secondary data of randomly selected fourty (40) publicly traded companies in Europe from four different industry groupings namely: manufacture of basic pharmaceuticals, manufacture of food products and beverages, information technology and manufacture of basic metals.

Condfidence in the future is a signicant factor for business development. However frequently, accurate and specific purposes are spread over the market environment influence.Thus,it is necessary to make an appropriate consideration of instability, which is peculiar to the dynamic development. Volatility, variance and standard deviation are used to characterize the deviation of the investigated quantity from mean value. Volatility is one of the main instruments to measure the risk of the asset. The increasing availability of financial market data has enlarged volatility research potential but has also encouraged research into longer horizon volatility forecasts. In this paper we investigate stock index volatility with respect to capitalization with help of GARCH-modelling. There are chosen three indexes of OMX Nordic Exchange for our research. The Nordic list segment indexes comprising Nordic Large Cap, Mid Cap and Small Cap are based on the three market capitalization groups. We implement GARCH-modeling for considering indexes and compare our results in order to conclude which ones of the indexes is more volatile. The OMX Nordic list indexis quiet new(2002)and reorganized as late as October 2006. The current value is now about 300 and no options do exist. In current work we are also interested in estimation of the Heston model(SVmodel), which is popular in financial world and can be used in option pricing in the future. The results of our investigations show that Large Cap Index is more volatile then Middle and Small Cap Indexes.

The famous Black-Scholes (BS) model used in the option pricing theory contains two parameters - a volatility and an interest rate. Both parameters should be determined before the price evaluation procedure starts. Usually one use the historical data to guess the value of these parameters. For short lifetime options the interest rate can be estimated in proper way, but the volatility estimation is, as well in this case, more demanding. It turns out that the volatility should be considered as a function of the asset prices and time to make the valuation self consistent. One of the approaches to this problem is the method of uncertain volatility and the static hedging. In this case the envelopes for the maximal and minimal estimated option price will be introduced. The envelopes will be described by the Black - Scholes - Barenblatt (BSB) equations. The existence of the upper and lower bounds for the option price makes it possible to develop the worse and the best cases scenario for the given portfolio. These estimations will be financially relevant if the upper and lower envelopes lie relatively narrow to each other. One of the ideas to converge envelopes to an unknown solution is the possibility to introduce an optimal static hedged portfolio.

In this paper we investigate pricing of variance swaps contracts. The literature is mostly dedicated to the pricing using replication with portfolio of vanilla options. In some papers the valuation with stochastic volatility models is discussed as well. Stochastic volatility is becoming more and more interesting to the investors. Therefore we decided to perform valuation with the Heston stochastic volatility model, as well as by using replication strategy. The thesis was done at SunGard Front Arena, so for testing the replica- tion strategy Front Arena software was used. For calibration and testing of the Heston model we used MatLab.

In this thesis, we propose two continuous time stochastic volatility models with long memory that generalize two existing models. More importantly, we provide analytical formulae that allow us to study option prices numerically, rather than by means of simulation. We are not aware about analytical results in continuous time long memory case. In both models, we allow for the non-zero correlation between the stochastic volatility and stock price processes. We numerically study the effects of long memory on the option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter in short memory models. We also find that long memory models have the potential to accommodate the short term options and the decay of volatility skew better than the corresponding short memory stochastic volatility models.

This paper aims to model and forecast the volatility of gold price with the help of other precious metals. The data applied for application part in the article involves three financial time series which are gold, silver and platinum daily spot prices. The volatility is modeled by univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models including GARCH and EGARCH with different distributions such as normal distribution and student-t distribution. At the same time, comparisons of estimation and forecasting the volatility between GARCH family models have been done.