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

Risk management with default-risky forwards

This paper studies the impact of counter-party default risk of forward contracts on a firm's production and hedging decisions. Using a model of a risk-averse competitive firm under price uncertainty, it derives several fundamental results. If expected profits from forward contracts are zero, the hedge ratio is surprisingly not affected by default risk under general preferences and general price distributions. This robustness result still holds if forwards are subject to additional basis risk. In general, the analysis shows that default risk is no valid reason to reduce hedge ratios if the size of a firm's forward position does not affect the counter-party's default probability. However, a firm's optimal output is negatively affected by default risk and it is generally advisable to hedge default risk with credit derivatives

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

Risk-adjusted option-implied moments

Option-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution, but are derived under the risk-neutral probability measure. This paper shows how to convert risk-neutral moments into the corresponding physical ones. The main theoretical result expresses moments under the physical probability measure in terms of observed option prices and the preferences of a representative investor. Based on this result, we investigate several empirical questions. We show that a model of a representative investor with CRRA utility can explain the variance risk premium for the S&P500 index but fails to capture variance and skewness risk premiums simultaneously. Moreover, we present methods to estimate forward-looking market risk premiums and investors' disappointment aversion implied in market prices

How to hedge if the payment date is uncertain?

This paper is the first to study the hedging of price risk with uncertain payment dates, a frequent problem in practice. It derives a variance-minimizing hedging strategy for two settings, the first employing linear contracts with different times to maturity and the second allowing for non-linear exotic derivatives. Using commodity prices and exchange rates, we empirically show the optimal strategy clearly outperforms heuristic alternatives in both settings. Non-linear instruments offer advantages with increasing hedge horizons and strongly dependent time and price risk, while linear instruments can suffice for short horizons and weak dependency

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