We extend the definition of a convex risk measure to a conditionalframework where additional information is available. We characterize these riskmeasures through the associated acceptance sets and prove a representationresult in terms of conditional expectations. As an example we consider the...

Option pricing models are calibrated to market data of plain vanillas by minimization of an error functional. From the economic viewpoint, there are several possibilities to measure the error between the market and the model. These different specifications of the error give rise to different...

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...

The introduction of derivatives on Bitcoin enables investors to hedge risk exposures in cryptocurrencies. Because of volatility swings and jumps in cryptocurrency prices, the traditional variance-based approach to obtain hedge ratios is infeasible. As a consequence, we consider two extensions of...

AI artificial intelligence brings about new quantitative techniques to assess the state of an economy. Here we describe a new measure for systemic risk: the Financial Risk Meter (FRM). This measure is based on the penalization parameter (λ) of a linear quantile lasso regression. The FRM is...

A flexible framework for the analysis of tail events is proposed. The framework contains tail moment measures that allow for Expected Shortfall (ES) estimation. Connecting the implied tail thickness of a family of distributions with the quantile and expectile estimation, a platform for risk...

A system of risk factors necessarily involves systemic risk. The analysis of systemic risk is in the focus of recent econometric analysis and uses tail event and network based techniques. Here we bring tail event and network dynamics together into one context. In order to pursue such joint...

Risk management and the thorough understanding of the relations between financial markets and the standard theory of macroeconomics have always been among the topics most addressed by researchers, both financial mathematicians and economists. This work aims at explaining investors' behavior from...

Weather influences our daily lives and choices and has an enormous impact on cooperate revenues and earnings. Weather derivatives differ from most derivatives in that the underlying weather cannot be traded and their market is relatively illiquid. The weather derivative market is therefore...

On the temperature derivative market, modeling temperature volatility is an important issue for pricing and hedging. In order to apply pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with...