This paper presents an estimation of Value at Risk (VaR) using Monte Carlo Simulation (MCS) under the symmetric GARCH (1,1) model in three different markets, United States, Eurozone and Japan, represented by the indexes Dow Jones Industrial Average, Euro Stoxx 50 and Nikkei 225 respectively,...

For risk management, implementing risk measures and backtesting them are essential tasks. Since the expected shortfall (ES) possesses coherence and tail sensitivity, the Basel Committee has raised the option to replace the classical risk measure value-at-risk (VaR) with ES. However, the...

The severity of extreme weather events is increasing due to climate change, giving rise to physical climate risk. However, physical climate risk is not only driven by the severity of individual hazards, but also by the interdependence of those hazards. This paper establishes bounds for the...

Stop-loss and limited loss random variables are two important transforms of a loss random variable and appear in many modelling problems in insurance, finance, and other fields. Risk levels of a loss variable and its transforms are often measured by risk measures. When only partial information...

The estimation of risk at extreme levels of significance (such as 0.1%) can be crucial to capture the losses during market downturns, such as the global financial crisis and the COVID-19 market crash. For many existing models, it is challenging to estimate risk at extreme levels of significance....

It is well known that volatility is time-varying and clustered. However, few studies have explored the information content of volatility clustering and its implications for investors’ risk aversion. This information is particularly important in turbulent periods, such as financial crisis. We...

We develop a utility and asset pricing theory that features a novel measure of tail risk. Our model determines investor demand for both left and right-tail risk premia from an indifference curve incorporating tolerance for variance and tail risk. We show that the systematic tail risk factors...

We demonstrate how a mixture of two SEP3 densities (skewed exponential power distribution of Fernández et al., 1995) can model the conditional forecasting of VaR and CVaR to efficiently cover market risk at regulatory levels of 1% and 2.5%, as well as at the additional 5% level. Our data...

Metaverses have been evolving following the popularity of blockchain technology. They build their own cryptocurrencies for transactions inside their platforms. These new cryptocurrencies are, however, still highly speculative, volatile, and risky, motivating us to manage their risk. In this...