A semiparametric factor model for electricity forward curve dynamics

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 parsimonious factor representation of the curve. Using closing prices from the Nordic power market Nord Pool we provide empirical evidence that the DSFM is an efficient tool for approximating forward curve dynamics.power market, forward electricity curve, dynamic semiparametric factor model

A semiparametric factor model for electricity forward curve dynamics

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 parsimonious factor representation of the curve. Using closing prices from the Nordic power market Nord Pool we provide empirical evidence that the DSFM is an efficient tool for approximating forward curve dynamics.power market, forward electricity curve, dynamic semiparametric factor model

Models for Heavy-tailed Asset Returns

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 normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation

Models for Heavy-tailed Asset Returns

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 normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation

DSFM fitting of Implied Volatility Surfaces

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 of high-dimensional data especially on an intra day level. The data reveal a degenerated string structure. Dynamic Semiparametric Factor Models (DSFM) are tailored to handle complex, degenerated data and yield low dimensional representation of the implied volatility surface (IVS). We discuss estimation issues of the model and apply it to DAX option prices.dynamic semiparametric factor model, implied volatility, vanilla options, DAX option prices

Models for Heavy-tailed Asset Returns

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 normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation;