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The 2008 financial crisis provides a valuable opportunity to study empirical data of market volatility during severe financial crisis. In this thesis, we study the implied volatility of VIX options during the crisis (2008) and a relatively calm period (2011). We present a method of calculating the implied volatility of VIX options and fit the implied volatilities using a 4th degree spline interpolation and propose method of extracting risk neutral density from fitted data. We analyze the slope and the level of the fitted implied volatility of VIX options during those periods. The results show that the level of the implied volatility of VIX options is higher and the slope is flatter during the distressed market compared to the relative calm periods.

There exist a lot of empirical researches, that examine what factors effect the stock market volatility. The concept of investor sentiment is quite popular and is frequently discussed. However, there does not exist any research which would study the relation between the change in election preferences during the presidential campaigns and stock market volatility. The present thesis explores the effect of political sentiment on United States and French models. Here, we construct the model, which examines the effect of change in election preferences on the volatility. The results suggest, that change in election preferences does not affect the stock market volatility during the presidential campaign. Thus, its inclusion to the model does not increase the prediction power.

House Price in Taiwan is very volatile during the past few decades. As Taiwan go into enormous boom, more and more amount of money invest in the house market. Although house investment is considered as a good investment tool with low risk and inflation hedge properties, its risk can not be underestimated. Therefore, by using the GARCH model, this paper tries to analyze volatilities of investment return in the Taipei housing market from 1973 to 2002. For existing housing, we are not able to use GARCH to model investment volatility because of uncorrelated term risks. On the contrary, pre-sale housing contains correlated term risk. We adopt ARMA(4,4)-GARCH(1,1) to model the investment volatility of pre-sale housing. The investment risk of pre-sale housing is not constant but is time-varying. When an unexpected event happened, the shock will persist but decay from 86 percent in the next term to 40 percent in the sixth term. And we can observe volatility cluster phenomenon from the graph of conditional variance. During 1973 to 1975¡B1979 to 1983 and 1987 to 1990, the risks are higher than other period. Because previous studies commonly suggest some structural changes in the Taiwan housing market, we also control the risk premium affected by the structural changes in our model. We found ARMA(4,4)-GARCH(1,1) can still model the investment volatility process of pre-sale housing, but there is no evidence of risk premium caused by structural changes.

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We use dynamic hedging to replicate the short put positions of common stocks and thelong put positions of equity index. The strategy is developed based on the fact that the volatility of average constituent stocks is greater than that of the index, and the aggregate movement of the constituent stocks becomes the movement of the index. Therefore, we expect the long-short volatility strategy to deliver stable returns. In this study, we first employ Monte Carlo simulation methods to create paths for the underlying securities and the corresponding index. Then, we use Black-Scholes delta-neutral dynamic hedging strategy to create synthetic options for the long-short put positions.Specifically, we conduct the dynamic replication strategy to form long put option of TSEC Taiwan 50 equity index and short options of its constituent stocks. Finally, we pick the TSECTaiwan Mid-Cap 100 Index and replicate the long-short volatility strategy again. This time the target constituents screening criteria are high beta and high historical volatility. The empirical studies show that: (1) The correlation coefficients between stock pairs are reciprocally related to the standard deviations of strategy returns. (2) The main source of losses is performance deviation of the price of small-sized stocks and the index. (3) The return of the strategy for portfolios excluding small cap stocks will be improved. (4) The loss will decline if we apply short strip strategy on those stocks which prices perform worse than the index. (5) The higher the volatility of the stocks we select, the greater the dynamic hedging premium we can get. (6) If we pick the high beta stocks to avoid the trend of stock prices diverging from the index, then the strategy yields higher returns.

This thesis presents five empirical papers investigating the issue of arbitrage trading of the FTSE 100 stock index futures. The first paper explores the effects of nonsynchronous trading on the spot index and develops a new technique as well as improving current methodologies for removing them. Studies in U. S. have shown that if the problem of non-synchronous trading is severe, the reported spot index is not reliable affecting the correct pricing of futures contracts. The second paper investigates the elasticity of supply of arbitrage in the futures market and the ability of the spot and the futures markets to respond to new information. It shows that arbitrage trading is initiated when spot prices largely drift apart from the futures prices. In addition, the futures prices tend to uncover new information before the spot prices, although this relationship is not stable over time. The analysis incorporates all possible channels of information to the -markets, which previous research fails to consider. The third paper analyses the behaviour of the deviation of the actual futures price from its theoretical value. Although this deviation is seen to have decreased its size over the years, it is still significant and persistent. Furthermore, it cannot be explained by the tax-timing option on pricing the futures or the effects of nonsynchronous trading. The fourth paper examines the presence, size and frequency of the profitability of the observed arbitrage opportunities by applying different transactions costs bounds to account for different classes of traders. After applying trading simulations arbitrage profitability is found to be frequent and significant, despite the fact that its size has decreased over the years. Finally, the thesis concludes with the fifth empirical paper which investigates the impact of futures trading on the spot and futures market volatility. It finds that arbitrage increases spot and futures price volatility but a volatile market brings the two markets closer on the whole, the thesis shows that although profitable arbitrage opportunities are not present in the long-run, they are not quickly removed in the short-run, allowing the spot and futures prices to drift apart.

With the rapid development of option markets throughout the world, option pricing has become an important field in financial engineering. Among a variety of option pricing models, volatility of underlying asset is associated with risk and uncertainty, and hence is treated as one of the key factors affecting the price of an option. In particular, in the framework of the Black-Scholes option pricing model, volatility of the underlying stock is the only unobservable variable, and has attracted a large amount of attention of both academics and practitioners. This thesis is concerned with the implied volatility in the Australian index option market. Two interesting problems are examined. First, the relation between implied volatility and subsequently realized volatility is investigated by using the S&P/ASX 200 (XJO) index options over a five-year period from April 2001 to March 2006. Unlike the S&P 100 index options in the US market, the XJO index options are traded infrequently, in low volumes, and with a long maturity cycle. This implies that the errors-in-variable problem for the measurement of implied volatility is more likely to exist. After accounting for this problem by the instrumental variable method, it is found that both call and put options implied volatilities are nearly unbiased and superior to historical volatility in forecasting future realized volatility. Second, the volatility structure implied by the XJO index options is examined during the period from April 2001 to June 2005. The volatility structure with respect to moneyness and time to maturity are investigated for both call and put option price series. It is found that the volatility smile largely exists, with call (put) option implied volatilities decreasing monotonically as the call (put) goes deeper out of the money (in the money). This result is consistent with the welldocumented evidence of volatility smile on other index options since the stock market crash of 1987. In summary, this thesis presents some important findings on the volatility inferred from the XJO index options traded on the ASX.

This thesis consists of three research topics, which together study the related topics of volatility jumps, modeling volatility and forecasting Value-at-­Risk (VaR). The first topic focuses on volatility jumps based on two recently developed jumps detection methods and empirically studied six markets and the distributional features, size and intensity of jumps and cojumps. The results indicate that foreign exchange markets have higher jump intensities, while equity markets have a larger jump size. I find that index and stock markets have more interdependent cojumps across markets. I also find two recently proposed jump detection methods deliver contradictory results of jump and cojump properties. The jump detection technique based on realized outlyingness weighted variation (ROWV) delivers higher jump intensities in foreign exchange markets, whereas the bi-­power variation (BV) method produces higher jump intensities in equity markets. Moreover, jumps under the ROWV method display more serial correlations than the BV method. The ROWV method detects more cojumps and higher cojumps intensities than the BV method does, particularly in foreign exchange markets. In the second topic, the Model Confidence Set test (MCS) is used. MCS selects superior models by power in forecasting ability. The candidate models set included 9 GARCH type models and 8 realized volatility models. The dataset is based on six markets spanning more than 10 years, avoiding the so-called data snooping problem. The dataset is extended by including recent financial crisis periods. The advantage of the MCS test is that it can compare models in a group, not only in a pair. Two loss functions that are robust to noise in volatility proxy were also implemented and the empirical results indicated that the traditional GARCH models were outperformed by realized volatility models when using intraday data. The MCS test based on MSE selected asymmetric ARFIMA models and the HAR mode as the most predictive, while the asymmetric QLike loss function revealed the leveraged HAR and leveraged HAR-­CJ model based on bi-­power variation as the highest performers. Moreover, results from the subsamples indicate that the asymmetric ARFIMA model performs best over turbulent periods. The third topic focuses on evaluating a broad band of VaR forecasts. Different VaR models were compared across six markets, five volatility models, four distributions and 8 quantiles, resulting in 960 specifications. The MCS test based on regulatory favored asymmetric loss function was applied and the empirical results indicate that the proposed asymmetric ARFIMA and leveraged HAR models, coupled with generalized extreme value distribution (GEV) or generalized Pareto distribution (GPD), have the superior predictive ability on both long and short positions. The filtered extreme value methods were found to handle not only extreme quantiles but also regular ones. The analysis conducted in this thesis is intended to aid risk management, and subsequently reduce the probability of financial distress in the sector.

This diploma thesis focuses on modeling volatility in financial time series. The main approach to modelling volatility is using GARCH models which can capture the variability of conditional volatility of time series. For modelling a conditional mean value in time series are used ARMA models. In the series there are usually not fulfilled the assumption of earnings normality, therefore, are the earnings in most cased characterized by the leptokurtic shape of distribution. The thesis introduces some more distribution types, which can be more easily used for the earnings distribution - above all the Students t distribution. The aim of the thesis in the first part is to present the topic of financial time series and description of the GARCH models including their further modification. There are used e.g. IGARCH or other models capturing asymmetric impact of shocks such as GJR-GARCH. The second part deals with generated data, where are more in detail explored the volatility models and their behavior in corresponding financial time series. The third part focuses on the volatility estimation and forecasting for the financial time series. Firstly this concerns development of stock index MICEX secondly currency pair Russian Ruble to Czech Crown and eventually price development of the Brent crude oil. The goal of the third part is to present the impacts on volatility of chosen time series applied on the example of economic sanctions against Russia after annexation of the Crimea peninsula which happened in the first quarter 2014.