Worst-case scenario portfolio optimization: a new stochastic control approach

We consider the determination of portfolio processes yielding the highest worst-case bound for the expected utility from final wealth if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. A particular application of our setting is to model crash scenarios where both the number and the height of the crash are uncertain but bounded. Also the situation of changing market coefficients after a possible crash is analyzed

Market depth and order size: an analysis of permanent price effects of DAX futures' trades

In this paper we empirically analyze the permanent price impact of trades by investigating the relation between unexpected net order flow and price changes. We use intraday data on German index futures. Our analysis based on a neural network model suggests that the assumption of a linear impact of orders on prices (which is often used in theoretical papers) is highly questionable. Therefore, empirical studies, comparing the depth of different markets, should be based on the whole price impact function instead of a simple ratio. To allow the market depth to depend on trade volume could open promising avenues for further theoretical research. This could lead to quite different trading strategies as in traditional models. --

The term structure of currency hedge ratios

Many firms face product price risk in foreign currency, uncertain costs in home currency and exchange rate risk. If prices and exchange rates in different countries interact, natural hedges of foreign exchange risk might result. If the effectiveness of such hedges depends on the hedge horizon, they might affect a firm's usage of foreign exchange derivatives and lead to a term structure of optimal hedge ratios. We analyze this issue by deriving the variance minimizing hedge position in currency forward contracts of an exporting firm that is exposed to different risks. In an empirical study, we quantify the term structure of hedge ratios for a ' typical ' German firm that is exporting either to the United States, the United Kingdom or Japan. Based on cointegrated vector autoregressive models of prices, interest rates and exchange rates, we show that the hedge ratio decreases substantially with the hedge horizon, reaching values of one half or less for a ten-years horizon. Our findings can (partly) explain the severe underhedging of long-term exchange rate exposures that is frequently observed and have important implications for the design of risk management strategies. --corporate risk management,foreign exchange risk,hedging,cointegrated VAR model

Model selection in neural networks

In this article we examine how model selection in neural networks can be guided by statistical procedures such as hypotheses tests, information criteria and cross validation. The application of these methods in neural network models is discussed, paying attention especially to the identification problems encountered. We then propose five specification strategies based on different statistical procedures and compare them in a simulation study. As the results of the study are promising, it is suggested that a statistical analysis should become an integral part of neural network modelling. --Neural Networks,Statistical Inference,Model Selection,Identification,Information Criteria,Cross Validation

Improving the pricing of options: a neural network approach

In this paper we apply statistical inference techniques to build neural network models which are able to explain the prices of call options written on the German stock index DAX. By testing for the explanatory power of several input variables serving as network inputs, some insight into the pricing process of the option market is obtained. The results indicate that statistical specification strategies lead to parsimonious networks which have a superior out-of-sample performance when compared to the Black/Scholes model. We further validate our results by providing plausible hedge parameters. --Option Pricing,Neural Networks,Statistical Inference,Model Selection

The term structure of illiquidity premia

This paper investigates the dynamics of the term structure of bond market illiquidity premia using data on German bond market segments which differ only with respect to their liquidity. We analyze the interaction between different parts of the term structure and identify economic factors that drive the illiquidity premia. We obtain three main results: (i) The term structure of illiquidity premia is U-shaped on average but its shape varies over time. (ii) There is a strict separation between the short end and the long end of the term structure of illiquidity premia, i.e. we find no evidence for spill-over effects across different maturities. Different economic factors drive different parts of the term structure. The short end is mainly driven by asset market volatilities which suggests a fight-to-liquidity effect. In contrast, the long end depends on long-term business cycle economic prospects. This suggests that different parts of the term structure are determined by different investor clienteles with different liquidity needs. (iii) There is a smooth transition from short-term to long-term illiquidity premia. The longer the time to maturity of a bond, the less important market volatilities are and the more important long-term economic prospects become. --bond liquidity,term structure of illiquidity premia

Hedging langfristiger Lieferverpflichtungen mit kurzfristigen Futures: Möglich oder unmöglich?

Die Arbeit unterscheidet sich in verschiedenen wesentlichen Punkten von vorliegenden Untersuchungen. Auf der theoretischen Ebene werden alle Hedgestrategien aus einem einheitlichen Modellrahmen abgeleitet. Einzelne Varianten ergeben sich dabei durch unterschiedliche Spezifikationen der mit dem Halten von Öl verbundenen Erträge, der sog. Convenience Yield. Überraschenderweise lassen sich verschiedene der in der Diskussion um die Metallgesellschaft vorgeschlagenen Hedgestrategien, so unterschiedlich sie auf den ersten Blick auch begründet sind, aus dem betrachteten Modellrahmen gewinnen. Im empirischen Teil liefert die vorliegende Studie den ersten umfassenden Vergleich fünf theoriegestützter Strategien zum Hedging einer Lieferverpflichtung von Rohöl auf Termin in zehn Jahren, der Grundstruktur des Hedgeproblems der MGRM. Da angesichts der im Vergleich zum langfristigen Hedgehorizont relativ kurzen Historie verfügbarer Spot- und Futurespreise eine historische Simulation wenig Aussagekraft hat, wird anhand vorhandener Spot- und Futurespreise ein Modell zur Simulation verschiedener Preisszenarien entwickelt. Auf Basis der Hedgeergebnisse für eine Vielzahl simulierter Szenarien erfolgt eine Beurteilung der zu erwartenden Erträge und Risken der Strategien. Umfangreiche Stabilitätsanalysen prüfen die Sensitivität der Hedgeergebnisse bezüglich der in die Hedge-Ratios eingehenden Parameter, des verwendeten Datenfensters, der Mean-Reversion der Spotpreise und des Hedgehorizontes

Market Depth and Order Size - An Analysis of Permanent Price Effects of DAX Futures' Trades

In this paper we empirically analyze the permanent price impact of trades by investigating the relation between unexpected net order flow and price changes. We use intraday data on German index futures. Our analysis based on a neural network model suggests that the assumption of a linear impact of orders on prices (which is often used in theoretical papers) is highly questionable. Therefore, empirical studies, comparing the depth of different markets, should be based on the whole price impact function instead of a simple ratio. To allow the market depth to depend on trade volume could open promising avenues for further theoretical research. This could lead to quite different trading strategies as in traditional models

Hedging langfristiger Lieferverpflichtungen mit kurzfristigen Futures: möglich oder unmöglich?

Im Laufe des Jahres 1993 war die Metallgesellschaft Refining & Marketing (MGRM), eine US-amerikanische Tochtergesellschaft der Metallgesellschaft AG, in großem Umfang die Verpflichtung eingegangen, langfristig Öl zu Festpreisen zu liefern. Das dadurch entstehende Preisrisiko sollte über Derivate reduziert bzw. ausgeschaltet werden. Da die vorgesehenen Liefertermine bis zu zehn Jahre in der Zukunft lagen, existierten keine laufzeitäquivalenten Ölderivate. Statt dessen kaufte die MGRM eine dem gesamten zukünftigen Liefervolumen entsprechende Anzahl von Terminkontrakten mit kurzer Laufzeit von meist nur einem Monat. Bei Fälligkeit wurden die Positionen in den nächsten kurz laufenden Kontrakt überrollt. Diese Hedgestrategie führte letztlich zu einer Krise des gesamten Konzerns, die im Dezember 1993 in der Ablösung des Vorstandes, der schrittweisen Auflösung der Ölgeschäfte und Verlusten in Milliardenhöhe gipfelte. --