A Simple Approach to Country Risk

The No-Arbitrage model by Schönbucher [30] is combined with the Extended Vasicek Term Structure Model and applied to the pricing of DM-Eurobonds issued by sovereigns from emerging economies. Practical hedging according to the model is investigated. A portfolio of DM-Eurobonds is analyzed using the risk measures "Shortfall" and "Value at Risk"

Eine Einführung in die arbitragefreie Bewertung von Derivaten in stetiger Zeit am Beispiel europäischer Devisenoptionen

An Introductory to Continuous-Scale Derivatives Evaluation in a Non-Arbitrage Environment on the Basis of the Example of European Foreign-Exchange Options The legendary evaluation formulae of Black/Scholes (1973) and Garman/Kohlhagen (1983) are explained in great detail in a didactically attractive manner. To begin with, two fundamental discoveries concerning the option price theory are explained with the help of a simple binomial model: independence of optionrights evaluations from market participants’ risk-acceptance propensity and the resultant possibility of evaluating option rights in an imaginary risk-free environment. This is followed by a model reflecting the dynamism of prices - Brown’s geometric progression. This is the basis of the Garman/Kohlhagen differential equation, which provides the justification of the two aforementioned fundamental discoveries pertaining to the continuous-scale evaluations. With the help of evaluations in a risk-free environment, the Garman/Kohlhagen formula is subsequently developed, which includes the Black /Scholes formula describing a special case. Reading this introductory presupposes nothing more than “A-level knowledge of mathematics”

Deep Learning Diagnostics ‒ How to Avoid Being Fooled by TensorFlow, PyTorch, or MXNet with the Help of Modern Econometrics

Training a Multi-Layer Perceptron (MLP) to achieve a minimum level of MSE is akin to doing Non-Linear Regression (NLR). Therefore, we use available econometric theory and the corresponding tools in R. Only if certain assumptions about the error term in the Data Generating Process are in place, may we enjoy the trained MLP as a consistent estimator. To verify the assumptions, careful diagnostics are necessary. Using controlled experiments we show that even in an ideal setting, an MLP may fail to learn a relationship whereas NLR performs better. We illustrate how the MLP is outperformed by Non-Linear Quantile Regression in the presence of outliers. A third situation in which the MLP is often led astray is where there is no relationship and the MLP still learns a relationship producing high levels of R². We show that circumventing the trap of spurious learning is only possible with the help of diagnostics

Backtesting von volatilitätsgesteuerten Aktienportfolios

Aktien spielen in der Asset-Allokation institutioneller Investoren üblicherweise eine bedeutsame Rolle. Eine Bedeutungszunahme erwächst zudem aus der Tatsache, dass verzinsliche Anlageformen angesichts des niedrigen Zinsniveaus aktuell nur geringe Ertragserwartungen aufweisen. Abbildung 1 verdeutlicht dies anhand ausgewählter Zinsinstrumente. Zunächst zeigen die Abbildungsbereiche (a) und (b), dass das Zinsniveau gemessen an 10-jährigen Swapsätzen und der Marktrendite eines globalen Anleihen-Indexes (BofA Merrill Lynch Global Broad Market Index) in wesentlichen Wirtschaftsräumen seit Jahren im Trend rückläufig ist. Anknüpfend stellt Abbildungsbereich (c) Boxplots zu empirischen Verteilungen der Zinskurven-Steilheiten dar. Erkennbar ist, dass zum jüngsten Betrachtungsstichtag die Übernahme von Zinsänderungsrisiken im Verhältnis zur eigenen Historie wenig bis moderat honoriert wird. Dass Aktieninvestments demgegenüber durchschnittlich höhere Erträge erwirtschaften, wird durch die Darstellungen in Abbildung 2 gestützt. Abbildungsbereich (a) zeigt, dass Aktien in den vergangenen 20 Jahren unter Anwendung rollierender 5-jähriger Halteperioden im Durchschnitt höhere annualisierte Renditen als Anleihen unter gleichen Bedingungen erzielen konnten. (...