DAX Futures Research Articles

Does Liquidity Matter When Crisis Is Brewing? Equity Returns and Intraday Liquidity in DAX Futures Market

Inspired by Mishkin (2011), we study a sample of high-frequency Eurex trading data from the peak of economic expansion preceding the global financial crisis of 2007-2009. Trading volume measures and bid￾ask spread in DAX futures market explain DAX equity returns. Advanced variable selection and multinomial model with survey analysis identify most important explanatory variables under specific market conditions. The index futures trading volume, along with bid-ask spread, identify extreme values of the underlying equity index returns. Further, the Markov Chain Monte Carlo (MCMC) model uncovers change points in the non-monotonic relationship between futures liquidity and the equity index returns, and identifies conditions leading to expected negative returns.

Hedging Bitcoin with conventional assets

The recent 50% drop in the price of the flagship cryptocurrency Bitcoin reinforces the persistent anxiety among cryptocurrency investors. Can alternative assets hedge Bitcoin risk? This study investigates the ability of equities, commodities, bonds, currencies, and VIX futures to hedge Bitcoin. Our in-sample analysis shows that the USDX, Gilt, Australian dollars, wheat, cocoa, cotton, sugar, copper, and lean hog can hedge Bitcoin, and the out-of-sample analysis reveals that the DAX, Dow-Jones, Nikkei, S&P 500, Brent, and WTI futures can be effective hedging instruments. We use a wavelet-based dynamic hedging model to account for heterogeneous investors in the Bitcoin market. For a short-term horizon, soybean futures reduce the variance in the in-sample hedged portfolio, and cotton futures offer the highest out-of-sample utility. Copper futures are the best for in-sample hedging in a long-term horizon, whereas live cattle futures have the best out-of-sample performance. These results show that conventional assets can hedge wild swings in Bitcoin.

Tail-risk protection trading strategies

Starting from well-known empirical stylized facts of financial time series, we develop dynamic portfolio protection trading strategies based on econometric methods. As a criterion for riskiness, we consider the evolution of the value-at-risk spread from a GARCH model with normal innovations relative to a GARCH model with generalized innovations. These generalized innovations may for example follow a Student t, a generalized hyperbolic, an alpha-stable or a Generalized Pareto distribution (GPD). Our results indicate that the GPD distribution provides the strongest signals for avoiding tail risks. This is not surprising as the GPD distribution arises as a limit of tail behaviour in extreme value theory and therefore is especially suited to deal with tail risks. Out-of-sample backtests on 11 years of DAX futures data, indicate that the dynamic tail-risk protection strategy effectively reduces the tail risk while outperforming traditional portfolio protection strategies. The results are further validated by calculating the statistical significance of the results obtained using bootstrap methods. A number of robustness tests including application to other assets further underline the effectiveness of the strategy. Finally, by empirically testing for second-order stochastic dominance, we find that risk averse investors would be willing to pay a positive premium to move from a static buy-and-hold investment in the DAX future to the tail-risk protection strategy.

Tail-Risk Protection Trading Strategies

Starting from well-known empirical stylised facts of financial time series, we develop dynamic portfolio protection trading strategies based on econometric methods. As a criterion for riskiness we consider the evolution of the value-at-risk spread from a GARCH model with normal innovations relative to a GARCH model with generalised innovations. These generalised innovations may for example follow a Student t, a generalized hyperbolic (GH), an alpha-stable or a Generalised Pareto (GPD) distribution. Our results indicate that the GPD distribution provides the strongest signals for avoiding tail risks. This is not surprising as the GPD distribution arises as a limit of tail behavior in extreme value theory and therefore is especially suited to deal with tail risks. Out-of-sample backtests on 11 years of DAX futures data, indicate that the dynamic tail-risk protection strategy effectively reduces the tail risk while outperforming traditional portfolio protection strategies. The results are further validated by calculating the statistical significance of the results obtained using bootstrap methods. A number of robustness tests including application to other assets further underline the effectiveness of the strategy. Finally, by empirically testing for second order stochastic dominance, we find that risk averse investors would be willing to pay a positive premium to move from a static buy-and-hold investment in the DAX future to the tail-risk protection strategy.

Hedging iTraxx credit default swap index trading on an intraday basis: an empirical study

We consider the equity and Bund futures as financial instruments to hedge standard 5Y iTraxx Europe Main and Crossover indexes. Our analysis is based on a four-month intraday time series for traded prices and quoted spreads, respectively. We find that a DAX futures based intraday hedging strategy is the most efficient one. While the cross-asset hedging strategy reduces the intraday market risks of iTraxx Europe positions, the overall hedging efficiency is limited.

Ultra‐High‐Frequency Algorithmic Arbitrage Across International Index Futures

ABSTRACTWe show that persistent lead–lag relationships spanning mere fractions of a second exist in all three possible pairings of the S&P 500, FTSE 100 and DAX futures contracts. These relationships exhibit clear intraday patterns which help us to forecast mid‐quote changes in lagging contracts with directional accuracy in excess of 85%. A simple algorithmic trading strategy exploiting these relations yields economically significant profits which are robust to market impact costs and the bid–ask spread. We find that price slippage and infrastructure costs are our most important limits to arbitrage. Our results support the impossibility of EMH view that informational inefficiencies incentivize arbitrageurs to eliminate mispricings. Copyright © 2014 John Wiley & Sons, Ltd.

The real benchmark of DAX index products and the influence of information dissemination: A natural experiment

Analysing 5 exchange traded funds (ETFs) and 26 index certificates, this is a comprehensive intraday study combining the perspective of information dissemination and pricing quality. We focus on the Volkswagen extreme event day on 28 October 2008, where a breakdown of the futures-cash arbitrage relationship offered the unique opportunity to identify the true benchmark of index-related products free from market microstructure noise. Although product information prospectuses promise to follow the DAX, we discover that the price quote level of DAX futures contracts became the one-on-one benchmark for all ETFs and for nearly all index certificates. We identify deviations between ETFs and their fair value exceeding 4 per cent. This is striking because the creation redemption process is assumed to restrict deviations. Analysing price information dynamics, we find that the revelation of new information to the market does not determine the price quote setting strategy of market makers during the extreme event. Hedging opportunities deliver a substantive argument to support the benchmark position of DAX futures.

A Partially Linear Approach to Modeling the Dynamics of Spot and Futures Prices

This paper considers the dynamics of spot and futures prices in the presence of arbitrage. A partially linear error correction model is proposed where the adjustment coefficient is allowed to depend nonlinearly on the lagged price difference. The model is estimated using data on the DAX index and the DAX futures contract. We find that the adjustment is indeed nonlinear. The linear alternative is rejected. The speed of price adjustment is increasing almost monotonically with the magnitude of the price difference. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:371–384, 2015

Hedging iTraxx CDS Index Trading on an Intraday Basis: An Empirical Study

In this paper we examine the effectiveness of intraday hedging models for CDS index trading by means of more liquidly traded exchange-based future contracts. We consider the equity and BUND future as financial instruments to hedge standard 5Y iTraxx Euro Main and Crossover indices. Our analysis is based on a 4-month intraday time series for traded prices and quoted spreads, respectively. We find that a DAX future based intraday hedging strategy is the most efficient one. While the cross-asset hedging strategy reduces the intraday market risks of iTraxx Euro positions, the overall hedging efficiency is limited.

Ultra High Frequency Statistical Arbitrage Across International Index Futures

We show that exploitable lead-lag relations of the order of a few hundred milliseconds exist in the three pairings between the S&P 500, FTSE 100, and DAX futures contracts. These relations exhibit clear intra-daily patterns, particularly around the US open, the European close, and the announcement of macroeconomic data. Using this information, we forecast mid-quote changes in lagging contracts with a directional accuracy in excess of 85%. A simple statistical arbitrage strategy exploiting these relations yields economically significant profits which are robust to market impact costs and the bid-ask spread. However, returns are sensitive to the risk of slippage, and the most profitable trading opportunities rarely exist for longer than 300 milliseconds. Hence, we highlight price slippage and infrastructure costs as the most significant limits to arbitrage in this market setting. Overall, our results accord with the view that informational inefficiencies incentivize arbitrageurs to appropriate pricing anomalies.

Intraday futures patterns and volume–volatility relationships: the German evidence

This paper examines the intraday behavior of 5-min DAX futures return volatility, volume and transactions, employing data from between January 1999 and September 2011, thus covering major market up and down trends. We focus on the interplay of the above variables finding a W-shape due to US macroeconomic news releases and the opening of US markets. By carefully modeling regular but infrequent events, we show that the last trading days of the FDAX and ODAX have significant impact on volatility and alter the intraday patterns. Additionally, we pay special attention to interactions between the futures and cash market caused by different trading hours at the Eurex. Thereby, we discover a uW-shape lending support for Daigler’s (J Futures Markets 17:45–74, 1997) extended market closure theory. Focusing on possible changes in the interplay of volume and volatility, we empirically analyze the implications of different volume–volatility theories. Finally, we model simultaneously the main volatility components—intraday calendar effects, macroeconomic announcement effects and interday volatility clustering—employing the framework of Andersen and Bollerslev (J Finance 53:219–265, 1998) to quantify and compare the impact of macroeconomic news announcements during contractions and expansions and focus on the economic impact of the crisis 2007/2008 on intraday volatility.

Model calibration and automated trading agent for Euro futures

We explored the application of a machine learning method, Logitboost, to automatically calibrate a trading model using different versions of the same technical analysis indicators. This approach takes advantage of boosting's feature selection capability to select an optimal combination of technical indicators and design a new set of trading rules. We tested this approach with high-frequency data of the Dow Jones EURO STOXX 50 Index Futures (FESX) and the DAX Futures (FDAX) for March 2009. Our method was implemented with different learning algorithms and outperformed a combination of the same group of technical analysis indicators using the parameters typically recommended by practitioners. We incorporated this method of model calibration in a trading agent that relies on a layered structure consisting of the machine learning algorithm described above, an online learning utility, a trading strategy, and a risk management overlay. The online learning layer combines the output of several experts and suggests a short or long position. If the expected position is positive (negative), the trading agent sends a buy (sell) limit order at prices slightly lower (higher) than the bid price at the top of the buy (sell) order book less (plus) transaction costs. If the order is not 100% filled within a fixed period (i.e. 1 minute) of being issued, the existent limit orders are cancelled, and limit orders are reissued according to the new experts' forecast. As part of its risk management capability, the trading agent eliminates any weak trading signal. The trading agent algorithm generated positive returns for the two major European index futures (FESX and FDAX) and outperformed a buy-and-hold strategy.

Extreme Börsenbewegung und Intraday-Preisstellung von Open-End-Turbo-Zertifikaten auf den DAX: Der Fall Kerviel

Am 21. Januar 2008 ist der DAX als Folge der Fehlspekulation des Aktienhandlers Jerome Kerviel bei der Societe Generale uber 7 % eingebrochen. Seit Auflegung der ersten Open End Turbo-Zertifikate im November 2001 markiert dieser Handelstag den hochsten prozentualen Tagesverlust. Diese klinische Studie analysiert fur diesen Crashtag die Intraday-Preisstellung der funf Emittenten fur Open End Turbo-Zertifikate auf den DAX. Im Ergebnis stellen wir okonomisch und statistisch signifikante Unterschiede in der Preisstellung zwischen den Emittenten fest. Die empirisch zu beobachtende relative Bewertungsdifferenz zwischen quotiertem Preis und fairem Wert ist zudem abhangig vom Hebel. Dieser ubt bei Long-Zertifikaten einen positiven Einfluss auf die relative Bewertungsdifferenz aus und umgekehrt bei Short-Zertifikaten. Die Emittenten weisen unterschiedliche Strategien bei der Anpassung der Breite der Geld-Briefspanne auf. Der relative Spread ist jeweils signifikant mit der relativen Bewertungsdifferenz korreliert. Die relative Differenz zwischen DAX und DAX-Futures verhalt sich invers zu der relativen Bewertungsdifferenz zwischen quotiertem Preis und fairem Wert bei Long-Zertifikaten und umgekehrt bei Short-Zertifikaten.

An Empirical Study on the Direct Hedge of DAX Futures in National Pension Fund of Investing DAX to Risk Management

An Empirical Study on the Direct Hedge of DAX Futures in National Pension Fund of Investing DAX to Risk Management

Time Scales in Futures Markets and Applications

The probability distribution of log-returns for financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of time series on futures. We show that the t-distribution with v=3 gives a nice description of almost all data series considered for a time scale Delta t below 1 hour. For Delta t 8 hours, the Gaussian regime is reached. A particular focus has been put on the DAX and Euro futures. This appears to be a quite general result that stays robust on a large set of futures, but not on any data sets. In this sense, this is not universal. A technique using factorial moments defined on a sequence of returns is described and similar results for time scales are obtained. Let us note that from a fundamental point of view, there is no clear reason why DAX and Euro futures should present similar behavior with respect to their return distributions. Both are complex markets where many internal and external factors interact at each instant to determine the transaction price. These factors are certainly different for an index on a change parity (Euro) and an index on stocks (DAX). Thus, this is striking that we can identify universal statistical features in price fluctuations of these markets. This is really the advantage of micro-structure analysis to prompt unified approaches of different kinds of markets. Finally, we examine the relation of power law distribution of returns with another scaling behavior of the data encoded into the Hurst exponent. We have obtained H=0.54 pm 0.04 for DAX and H=0.51 pm 0.03 for Euro futures.

Price Discovery and Information Transmission Processes Among Asset Markets: An Ultrahigh-Frequency Perspective

This paper examines the intra-day price discovery processes of the German bond, stock, and the U.S. dollar-Euro FX markets. We extend the methodology of Andersen, Bollerslev, Diebold, and Vega (2007) to analyze the effects of German, EMU, and U.S. macroeconomic announcements on return, volatility, and trading volume based on ultrahigh-frequency, i.e. one-minute and five second sampling intervals. More important, we study the inter-market transmissions among the three asset markets conditional on the release time of macroeconomic announcements. For both the pre-crisis and the 2007-08 subprime and financial crisis sub-sample periods, U.S. macroeconomic indicators show the strongest impact on return, volatility, and trading volume, while EMU announcements having almost no influence. News impacts are the strongest (weakest) for the DAX futures (U.S. dollar-Euro exchange rate). However, unlike the other two asset markets the FX market was not affected by the crisis. In addition, the information among the three markets transmits differently across the two subsamples. While the FX market is highly endogenous, Bund futures returns are positively affected by FX and DAX futures returns are negatively correlated with the Bund futures.

Intraday pricing of ETFs and certificates replicating the German DAX index

The market for the leading German equity index DAX comprises electronically traded futures contracts, fully replicated and swap-based exchange-traded funds (ETFs), and certificates. This paper reveals that DAX futures contracts contribute an economically and statistically significant proportion to contemporaneous price quotes of ETFs and certificates. This finding is surprising because the prospectus of ETFs and certificates claim to follow the stock index solely, but not the index futures contract. Exploring further the short-run dynamics, our results suggest that fully replicated ETFs cope better with adjusting their prices to the DAX index than swap-based ETFs and certificates.

A High‐Frequency Investigation of the Interaction between Volatility and DAX Returns

Abstract One of the most noticeable stylised facts in finance is that stock index returns are negatively correlated with changes in volatility. The economic rationale for the effect is still controversial. The competing explanations have different implications for the origin of the relationship: Are volatility changes induced by index movements, or inversely, does volatility drive index returns? To differentiate between the alternative hypotheses, we analyse the lead‐lag relationship of option implied volatility and index return in Germany based on Granger causality tests and impulse‐response functions. Our dataset consists of all transactions in DAX options and futures over the time period from 1995 to 2005. Analyzing returns over 5‐minute intervals, we find that the relationship is return‐driven in the sense that index returns Granger cause volatility changes. This causal relationship is statistically and economically significant and can be clearly separated from the contemporaneous correlation. The largest part of the implied volatility response occurs immediately, but we also observe a smaller retarded reaction for up to one hour. A volatility feedback effect is not discernible. If it exists, the stock market appears to correctly anticipate its importance for index returns.

Switching Phenomena in a System with No Switches

It is widely believed that switching phenomena require switches, but this is ac- tually not true. For an intriguing variety of switching phenomena in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fash- ion. For example, financial market fluctuations are characterized by many abrupt switch- ings creating increasing trends ("bubble formation") and decreasing trends ("financial col- lapse"). Such switching occurs on time scales ranging from macroscopic bubbles persisting for hundreds of days to microscopic bubbles persisting only for a few seconds. We ana- lyze a database containing 13,991,275 German DAX Future transactions recorded with a time resolution of 10 msec. For comparison, a database providing 2,592,531 of all S&P500 daily closing prices is used. We ask whether these ubiquitous switching phenomena have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the volatility after each switching occurs. We interpret our findings as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in transaction volume and time intervals between trades. We show that these financial market switching processes have properties similar to those of phase transitions. We suggest that the well-known catastrophic bubbles that occur on large time scales—such as the most recent financial crisis—are no outliers but single dramatic representatives caused by the switching

Price Formation in Spot and Futures Markets: Exchange Traded Funds vs. Index Futures

This article examines the issue of price leadership between a derivative and its underlying—in this case, the German DAX index and an exchange-traded fund (ETF) based on the DAX portfolio of stocks. Previous researchers had found that changes in DAX futures prices led movements in the underlying DAX index. Schlusche tests to see whether that result carries over to DaxEx, the DAX ETF traded on the EUREX exchange. He shows that both markets contribute to price discovery, but the influence of the DAX futures is about three times greater than the influence of the ETF. Digging more deeply into the relationship, he finds that the relative importance of the two markets in price determination varies over time, with the ETF carrying greater weight in times of higher volatility, while variations in relative trading volume, which he takes to be a measure of relative liquidity, do not seem to matter.