The GARCH model estimates the volatility of a time series. Information criteria are often used to determine orders of the GARCH model, although their suit- ability is not known. This thesis focuses on the order selection of the GARCH model using information criteria. The simulation study investigates whether in- formation criteria are appropriate for the model selection and how the selection depends on the order, number of observations, distribution of innovations, estima- tion method or model parameters. The predictive capabilities of models selected by information criteria are compared to the true model. 1

The equity option expiration effect is a well observed phenomenon and is explained by delta hedge rebalancing and pinning risk, which makes the strike price of an option work as a magnet for the underlying price. The FX option expiration effect has not previously been explored to the same extent. In this paper the FX option expiration effect is investigated with the aim of finding out whether it provides valuable information for predicting FX rate movements. New models are created based on the concept of the option relevance coefficient that determines which options are at higher risk of being in the money or out of the money at a specified future time and thus have an attraction effect. An algorithmic trading strategy is created to evaluate these models. The new models based on the FX option expiration effect strongly outperform time series models used as benchmarks. The best results are obtained when the information about the FX option expiration effect is included as an exogenous variable in a GARCH-X model. However, despite promising and consistent results, more scientific research is required to be able to draw significant conclusions. / Effekten av aktieoptioners förfall är ett välobserverat fenomen, som kan förklaras av delta hedge-ombalansering och pinning-risk. Som följd av dessa fungerar lösenpriset för en option som en magnet för det underliggande priset. Effekten av FX-optioners förfall har tidigare inte utforskats i samma utsträckning. I denna rapport undersöks effekten av FX-optioners förfall med målet att ta reda på om den kan ge information som kan användas till prediktioner av FX-kursen. Nya modeller skapas baserat på konceptet optionsrelevanskoefficient som bestämmer huruvida optioner har en större sannolikhet att vara "in the money" eller "out of the money" vid en specificerad framtida tidpunkt och därmed har en attraktionseffekt. En algoritmisk tradingstrategi skapas för att evaluera dessa modeller. De nya modellerna baserade på effekten av FX-optioners förfall överpresterar klart jämfört med de tidsseriemodeller som användes som riktmärken. De bästa resultaten uppnåddes när informationen om effekten av FX-optioners förfall inkluderas som en exogen variabel i en GARCH-X modell. Dock, trots lovande och konsekventa resultat, behövs mer vetenskaplig forskning för att kunna dra signifikanta slutsatser.

This research investigates to what extent the ARCH model and the GARCH model forecasts one-day-ahead out-of-sample daily volatility (conditional variance) in European AT1 CoCo bonds compared to the Random Walk model. The research also investigates how different orders of ARCH and GARCH models affect the forecasting accuracy. Specifically, the models investigated are the Random Walk model, ARCH(1), ARCH(2), ARCH(3), GARCH(1,1), GARCH(1,2), GARCH(2,1), and the GARCH(2,2)model. The data set used in this report is 47 European AT1 CoCo bonds from 20 different issuers.The results show that 42 out of 47 CoCo bonds have daily log returns that are conditional heteroscedastic. Five CoCo bonds with homoscedastic daily log returns were CoCo bonds with significant low liquidity. The results show that the GARCH model outperforms both the Random Walk model and the ARCH model, under the assumption that the innovations follow a normal distribution. The results also show that a higherorder of ARCH or GARCH does not necessarily lead to more accurate forecasts. The GARCH(1,1) model provided the most accurate predictions. The conclusion is that the GARCH models provide accurate volatility forecasts in CoCo bonds compared to the ARCH-model, and the Random Walk model. However, the ARCH model and the GARCH model fail to forecast the daily volatility in CoCo bondswith insufficient liquidity. Furthermore, a higher order of ARCH or GARCH models does not necessarily lead to better forecast results. / Denna uppsats undersöker till vilken utsträckning som ARCH och GARCH-modeller kan prediktera daglig volatilitet i AT1 CoCo-obligationer (eng. Additional Tier-1 Contingent Convertible Bonds), jämfört med Random Walk-modellen. Uppsatsen undersöker även hur olika parametrar I ARCH och GARCH-modeller påverkar resultatet i prediktionerna. De modeller som undersöks är Random Walk-modellen, ARCH(1), ARCH(2), ARCH(3), GARCH(1,1), GARCH(1,2), GARCH(2,1), och GARCH(2,2)-modellen. Datasetet som har använts i denna forskning består av 47 Europeiska AT1 CoCo obligationer från 20 olika emittenter. Resultatet visar att 42 av 47 CoCo-obligationer har betingat heteroskedastisk daglig avkastningsdata. Fem CoCo-obligationer med homoskedastisk avkastningsdata är obligationer med signifikant låg likviditet. Vidare visar resultatet visar att GARCH modellen överpresterar jämfört med både Random Walk-modellen och ARCH-modellen, under antagandet att innovationstermen följer en normal distribution. Resultatet visar även att en högre ordning av ARCH eller GARCH inte nödvändigtvis leder till ett bättre resultat i prediktonerna. GARCH(1,1)-modellen är modellen som predikterar den dagliga volatiliten i CoCo-obligationerna med bäst resultat. Slutsatsen är att GARCH-modellen predikterar volatiliteten i CoCo-obligationer bättre jämfört med ARCH-modellen och Random Walk-modellen. Däremot kan inte ARCH-modellen eller GARCH-modellen modellera CoCo-obligationer med signifikant låg likviditet. Vidare så medför en högre ordning i ARCH eller GARCH-modellen inte nödvändigtvis till bättre prediktioner.

The recent period of intensified electricity price volatility has challenged both private households and businesses, resulting in companies transitioning their strategies to address the uncertainties that follow. No previous study has analysed how electricity price volatility affects Swedish industries’ returns and electricity usage. Therefore, this essay aims to fill this knowledge gap and capture the impact of electricity price volatility on two different industries, one more electricity-intensive industry and one less electricity-intensive industry. By applying a DCC-GARCH model, the study examines the impact on the returns and electricity usage of two industries to analyse if electricity price volatility has affected businesses in terms of returns and electricity consumption.  The first DCC model was run on weekly electricity spot price data from Nord Pool and data constructed through a proxy of each industry’s average return. The results show that there is almost zero conditional correlation over time, ranging from 0.03 to 0.045, between the electricity price and each industry’s returns. There are no short-run spillover effects from electricity price volatility on the on the industries’ average returns. On the other hand, there is a long term spillover effect from electricity prices to the more electricity-intensive industry and no long term spillover for the less electricity-intensive industry.  The second DCC-GARCH modell is applied on monthly electricity spot prices from Nord Pool and data of monthly electricity usage of each industry. The industries are sorted by Swedish Standard Industrial Classification (SNI). SNI 17 stands for manufacture of paper and paper products and SNI 24 stands for manufacture of basic metals. The results from this part indicates that the dynamic conditional correlation between electricity price and the electricity usage in the paper industry is close to zero which differ from the basic metal industry which is positive. Beyond the dynamic conditional correlation, we find a short-term spillover effect from electricity price volatility to electricity usage in the basic metal industry, which is absent in the paper industry. On the other hand, there is a long-term spillover effect from electricity price volatility to electricity usage in the paper industry, which is absent for the electricity usage in basic metal industry.  Overall, our study shows that the businesses in the return proxy have preformed relatively well despite an uncertain period of volatile electricity prices. Simultaneously we find that the results for the industries electricity usage differ between the chosen industries.

Most of the notations and terminological conventions used in this thesis are Statistical. The aim in risk management is to describe the risk factors present in time series. In order to group these risk factors, one needs to distinguish between different stochastic processes and put them into different classes. The risk factors discussed in this thesis are fat tails and mean reversion. The presence of these risk factors fist need to be found in the historical dataset. I will refer to the historical dataset as the original dataset. The Ljung- Box-Pierce test will be used in this thesis to determine if the distribution of the original dataset has mean reversion or no mean reversion. / Mathematical Sciences / M.Sc. (Applied Mathematics)

This thesis will investigate if adding an exogenous variable (implied volatility) to the variance equation will increase the performance for the GARCH(1,1) and EGARCH(1,1) models based on the OMXS30 index. These models are also compared with the implied volatility itself as a forecasting/modeling method. To evaluate the models the realized variance will be used as an unbiased estimator of the conditional variance. The findings suggest that adding implied volatility to the variance equation increase the overall performance.

This thesis deals with various issues regarding determinants of US corporate credit spreads. These spreads are estimated as the difference between yields to maturity for corporate bonds and default-free instruments (Treasury bonds) of the same maturity. Corporate credit spreads are considered as measures of default risk. However, the premium required by investors for holding risky rather than risk-free bonds will incorporate a compensation not only for the default risk but also for other factors related to corporate bonds such as market liquidity or tax differential between corporate and Treasury bonds. In this study we firstly examine the relationship between bond ratings and credit spreads given that bond rating changes are expected to carry some informational value for debt investors. The findings indicate that bond ratings generally carry some informational value for corporate bond investors. The Granger causal relationship is more evident for negative watch lists and during periods of uncertainty in financial markets. In line with previous studies, our results suggest that changes in credit spreads are significantly related to interest rate levels, systematic risk factors (Fama and French) factors and equity returns.

Σκοπός της παρούσας μελέτης είναι να εξετάσουμε την σχέση που υπάρχει μεταξύ της χρηματιστηριακής αγοράς και αυτής των αποδόσεων των ομολόγων σε τέσσερις χώρες της Ευρωπαϊκής Ένωσης (Γερμανίας, Ιταλίας, Ισπανίας και Γαλλίας) για την περίοδο από τον Δεκέμβριο 1999 έως τον Δεκέμβριο του 2012. Προσπαθήσαμε να εξετάσουμε το κατά πόσο υπάρχουν συσχετίσεις μεταξύ των δύο περιουσιακών στοιχείων σε μεγάλο χρονικό διάστημα χρησιμοποιώντας πολυμεταβλητά μοντέλα. Τα δεδομένα που πήραμε είναι οι ημερήσιες αποδόσεις των 10ετών ομολόγων και τα κλεισίματα των χρηματιστηριακών αγορών των χωρών αυτών για κάθε μία ξεχωριστά. Ξεκινάμε την ερευνά μας χρησιμοποιώντας το μοντέλο του GARCH του Bollerslev (1990). Τέλος μέσω της συνολοκλήρωσης με την διαδικασία του Johansen test θα εξετάσουμε το κατά πόσο οι σειρές μας ολοκληρώνονται μακροχρόνια επηρεάζοντας η μία την άλλη καθώς και την μεταξύ τους εξάρτηση και την αιτιότητα των εν λόγω σχέσεων. Η εργασίας μας έχει ως στόχο να μας δείξει το κατά πόσο υπάρχει μακροχρόνια συσχέτιση μεταξύ των δύο αυτών αγορών, ώστε να βοηθά τους διαχειριστές και οικονομικούς αναλυτές να δημιουργούν το χαρτοφυλάκιο με το μικρότερο κίνδυνο και την μεγαλύτερη απόδοση. Τα αποτελέσματα μας δείχνουν μία μακροχρόνια συσχέτιση μεταξύ αυτών των δύο αγορών και ότι η μία αγορά επηρεάζει την άλλη σε βάθος χρόνου, οπότε είναι χρήσιμο σε ένα χαρτοφυλάκιο να υπάρχουν και τα δύο περιουσιακά στοιχεία. / The purpose of this study is to look at the relationship between stock market and bond market in four European Countries (Germany, France, Spain and Italy) for the period of December 1999 to December 2012. We attempt to examine whether the correlations between two classes of assets are time varying by using multivariate conditional volatility models. The data we are daily yields on 10-year bonds and the closures of the stock markets of these countries for each one individually. We start our investigation by applying GARCH model of Bollerslev (1990). Finally, through co integration with the process of Johansen test will look at whether our series completed long influencing each other and their mutual dependence and causality of these relations. Our paper aims to show us whether there is a long correlation between these two markets in order to help managers and financial analysts to create a portfolio with less risk and greater efficiency. Our results show a long-term correlation between these two markets and one market affects the other in the long run, so it is useful to have a portfolio of both assets.

Stock market volatility has been an important subject in the finance literature for which now an enormous body of research exists. Volatility modelling and forecasting have been in the epicentre of this line of research and although more than a few models have been proposed and key parameters on improving volatility forecasts have been considered, finance research has still to reach a consensus on this topic. This thesis enters the ongoing debate by carrying out empirical investigations by comparing models from the current pool of models as well as exploring and proposing the use of further key parameters in improving the accuracy of volatility modelling and forecasting. The importance of accurately forecasting volatility is paramount for the functioning of the economy and everyone involved in finance activities. For governments, the banking system, institutional and individual investors, researchers and academics, knowledge, understanding and the ability to forecast and proxy volatility accurately is a determining factor for making sound economic decisions. Four are the main contributions of this thesis. First, the findings of a volatility forecasting model comparison reveal that the GARCH genre of models are superior compared to the more ‘simple' models and models preferred by practitioners. Second, with the use of backward recursion forecasts we identify the appropriate in-sample length for producing accurate volatility forecasts, a parameter considered for the first time in the finance literature. Third, further model comparisons are conducted within a Value-at-Risk setting between the RiskMetrics model preferred by practitioners, and the more complex GARCH type models, arriving to the conclusion that GARCH type models are dominant. Finally, two further parameters, the Volatility Index (VIX) and Trading Volume, are considered and their contribution is assessed in the modelling and forecasting process of a selection of GARCH type models. We discover that although accuracy is improved upon, GARCH type forecasts are still superior.

In the first chapter, I analyze the question that whether the elasticity of intertemporal substitution or risk aversion is more important determinant of precautionary savings. This is an important question since a significant fraction of the capital accumulation is due to precautionary savings according to studies. Thus, knowing the important determinant of precautionary savings will be helpful to understand the capital accumulation mechanism. I look into the effects of the elasticity of intertemporal substitution and risk aversion on precautionary savings separately by performing simulations in order to obtain numerical results. I find that the elasticity of intertemporal substitution is more important determinant than risk aversion. In the second chapter, I study the impact of the introduction of futures trading on the volatility of the underlying spot market for Turkish Istanbul Stock Exchange (ISE).The economic literature intensified the debate on the negative or positive impact of futures trading on the stock market volatility. Although there are empirical studies for different countries with mixed results, most of them focus on developed countries. There are a few empirical researches on emerging markets. Analyzing the data, following results are obtained for ISE. First, the results suggest that the introduction of futures trading has decreased the volatility of ISE. Second, the results show that futures trading increases the speed at which information is impounded into spot market prices. Third, the asymmetric responses of volatility to the arrival of news for ISE have increased after the introduction of futures trading. In the third chapter, I investigate the presence of calendar anomalies in ISE by using GARCH models. The presence of calendar anomalies and their persistence presence since their first discovery still remains a puzzle to be solved. On the other hand, there are some claims that general anomalies are much less pronounced after they became known to the public. Most of the studies have examined the developed financial markets. However, it is important to test the calendar effects in data sets that are different from those in which they are originally discovered and so ISE is a good case to test the calendar effects for a developing country. / text