We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. A suitable regularity...

The implied volatility became one of the key issues in modern quantitative finance, since the plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount...

In this paper we introduce the dynamic semiparametric factor model (DSFM) for electricity forward curves. The biggest advantage of our approach is that it not only leads to smooth, seasonal forward curves extracted from exchange traded futures and forward electricity contracts, but also to a...

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a...

In this paper we introduce the dynamic semiparametric factor model (DSFM) for electricity forward curves. The biggest advantage of our approach is that it not only leads to smooth, seasonal forward curves extracted from exchange traded futures and forward electricity contracts, but also to a...

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel...