This paper implements different approaches used to compute the one-day Value-at-Risk (VaR) forecast for a portfolio of four currency exchange rates. The concepts and techniques of the conventional methods considered in the study are first reviewed. These approaches have shortcomings and therefore fail to capture the stylized characteristics of financial time series returns such as; non-normality, the phenomenon of volatility clustering and the fat tails exhibited by the return distribution. The GARCH models and its extensions have been widely used in financial econometrics to model the conditional volatility dynamics of financial returns. The paper utilizes a conditional extreme value theory (EVT) based model that combines the GJR-GARCH model that takes into account the asymmetric shocks in time-varying volatility observed in financial return series and EVT focuses on modeling the tail distribution to estimate extreme currency tail risk. The relative out-of-sample forecasting performance of the conditional-EVT model compared to the conventional models in estimating extreme risk is evaluated using the dynamic backtesting procedures. Comparing each of the methods based on the backtesting results, the conditional EVT-based model overwhelmingly outperforms all the conventional models. The overall results demonstrate that the conditional EVT-based model provides more accurate out-of-sample VaR forecasts in estimating the currency tail risk and captures the stylized facts of financial returns.

Cryptocurrencies have become increasingly popular in recent years attracting the attention of the media, academia, investors, speculators, regulators, and governments worldwide. This paper focuses on modelling the volatility dynamics of eight most popular cryptocurrencies in terms of their market capitalization for the period starting from 7th August 2015 to 1st August 2018. In particular, we consider the following cryptocurrencies; Bitcoin, Ethereum, Litecoin, Ripple, Moreno, Dash, Stellar and NEM. The GARCH-type models assuming different distributions for the innovations term are fitted to cryptocurrencies data and their adequacy is evaluated using diagnostic tests. The selected optimal GARCH-type models are then used to simulate out-of-sample volatility forecasts which are in turn utilized to estimate the one-day-ahead VaR forecasts. The empirical results demonstrate that the optimal in-sample GARCH-type specifications vary from the selected out-of-sample VaR forecasts models for all cryptocurrencies. Whilst the empirical results do not guarantee a straightforward preference among GARCH-type models, the asymmetric GARCH models with long memory property and heavy-tailed innovations distributions overall perform better for all cryptocurrencies.

Claims experience in non-life insurance is contingent on random eventualities of claim frequency and claim severity. By design, a single policy may possibly incur more than one claim such that the total number of claims as well as the total size of claims due on any given portfolio is unpredictable. For insurers to be able to settle claims that may occur from existing portfolios of policies at some future time periods, it is imperative that they adequately model historical and current data on claims experience; this can be used to project the expected future claims experience and setting sufficient reserves. Non-life insurance companies are often faced with two challenges when modeling claims data; selecting appropriate statistical distributions for claims data and establishing how well the selected statistical distributions fit the claims data. Accurate evaluation of claim frequency and claim severity plays a critical role in determining: An adequate premium loading factor, required reserve levels, product profitability and the impact of policy modifications. Whilst the assessment of insurers' actuarial risks in respect of their solvency status is a complex process, the first step toward the solution is the modeling of individual claims frequency and severity. This paper presents a methodical framework for choosing a suitable probability model that best describes automobile claim frequency and loss severity as well as their application in risk management. Selected statistical distributions are fitted to historical automobile claims data and parameters estimated using the maximum likelihood method. The Chi-square test is used to check the goodness-of-fit for claim frequency distributions whereas the Kolmogorov-Smirnov and Anderson-Darling tests are applied to claim severity distributions. The Akaike information criterion (AIC) is used to choose between competing distributions. Empirical results indicate that claim severity data is better modeled using heavy-tailed and skewed distributions. The lognormal distribution is selected as the best distribution to model the claim size while negative binomial and geometric disHow to cite this paper:

In this paper the generalized autoregressive conditional heteroscedastic models are applied in modeling exchange rate volatility of the USD/KES exchange rate using daily observations over the period starting 3 rd January 2003 to 31 st December 2015. The paper applies both symmetric and asymmetric models that capture most of the stylized facts about exchange rate returns such as volatility clustering and leverage effect. The performance of the symmetric GARCH (1, 1) and GARCH-M models as well as the asymmetric EGARCH (1, 1), GJR-GARCH (1, 1) and APARCH (1, 1) models with different residual distributions are applied to data. The most adequate models for estimating volatility of the exchange rates are the asymmetric APARCH model, GJR-GARCH model and EGARCH model with Student's t-distribution.

The recent global pandemic of coronavirus (COVID-19) has had an enormous impact on the financial markets across the world. It has created an unprecedented level of risk uncertainty, prompting investors to impetuously dispose of their assets leading to significant losses over a very short period. In this paper, the conditional heteroscedastic models and extreme value theory are combined to examine the extreme tail behaviour of stock indices from major economies over the period before and during the COVID-19 pandemic outbreak. Daily returns data of stock market indices from twelve different countries are used in this study. The paper implements a dynamic method for forecasting a one-day ahead Value at Risk. As a first step, a comprehensive in-sample volatility modelling is implemented with skewed Student's-t distribution assumption and their goodness of fit is determined using information selection criteria. In the second step, the VaR quantiles are estimated with the help of conditional Extreme Value Theory framework and then used to estimate the out-of-sample VaR forecasts. Backtesting results suggest that the conditional EVT based models consistently produce a better 1-day VaR performance compared with conditional models with asymmetric probability distributions for return innovations and maybe a better option in the estimation of VaR. This emphasizes the importance of modelling extreme events in stock markets using conditional extreme value theory and shows that the ability of the model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.