Final Report Summary - PRICE JUMP DYNAMICS (Price jump dynamics and evolution of market panic) IntroductionThe main aim of research project was to study the dynamics of extreme price movements, or price jumps, using high-frequency data of financial assets. Price jumps can be connected to important issues in market micro-structure, such as the efficiency of price formation, the provision of liquidity or the interaction between market players. From the practical point of view, traders are also interested in analysing price jumps since jumps are an important component of volatility and thus contributing to large losses/gains. Price jumps can be also used as a proxy to evaluate market (in)efficiency, to model information flows across markets including market panic or changes in the information driven trading. In this project, we focus in particular on the dynamics of price jumps in financial markets and in modelling the collective formation of price jumps over time series for multiple assets (e.g. all components of a particular stock market index) to describe phenomena like market panic or herding behaviour. The price jump dynamics also serves as a framework measuring the degree of integration of different markets and/or industry sectors and thus helps proposing better regulatory measures. ResultsThe main results of the studies can be summarised as follows.First, we introduced the notions of co-jumps and co-arrivals within the co-features framework. We formulated the limiting properties of co-jumps and discuss their discrete sample properties. In the presence of idiosyncratic price jumps, we identified the notion of weak co-jumps. We then introduced the notion of co-arrivals where the feature is the price jump arrival irrespective of the magnitude. We illustrated the proposed framework using the constituents of the DJIA30 over 01/01/2010 to 30/06/2012 and discuss the role of the multiple testing bias. Second, we extended the notion of co-jumps and co-arrivals to a novel theoretical framework for modelling mixed-frequency multivariate time series. The proposed methodology was constructed to identify commonalities, defined in terms of co-arrivals and co-jumps, sampled at high-frequency, to be explained with predictors sampled at lower frequency. We employed this framework to study the 10-year high-frequency European government bond yields as a function of low-frequency macro-factors, capturing the prevailing state of the economy, plus macro-announcements and bond auctions. Both idiosyncratic and common jump arrivals were found statistically significant, with the idiosyncratic arrivals more sensitive to financial distress characterised by a low level of commonality and correlation in jump arrivals.Third, we proposed a theoretical framework to predict the price jump arrivals in a multivariate likelihood framework. We employ the high-frequency European government bonds and the extensive set of news announcements to identify the significant predictors for European price jump arrivals. Further, we extended the framework to capture the causality across the European bond markets and estimated the parameters of the price jump contagion.We then focused on the price behaviour in new European Union (EU) emerging markets in Central and Eastern Europe and analysed their link to macroeconomic news announcements and price jumps. We presented new empirical evidence which shows that emerging EU markets react to news announcements with a delay and foreign macroeconomic news is mostly responsible for price jumps. A significant information transfer of price jumps from EU and U.S. markets is also noted. Despite the fact the emerging markets studied are an integral part of the EU, a much stronger influence results from U.S. markets, especially when controlling for spill-over effects. The presence of U.S.-based investors on these markets can explain this result. Further, we focused on the behaviour of the Prague Stock Exchange and response of the traded assets to financial distress. In particular, we employed the high-frequency data from Prague Stock Exchange (PSE) and New York Stock Exchange (NYSE) to analyse the variation in extreme price movements and market volatility around the period of fall of Lehman Brothers. The sample ranges from January 2008 to July 2009. We employed the price jump indicators optimal with respect to Type-I and Type-II errors. The former one showed an increase in market volatility and extreme price movements during financial distress, while the later extracted the information on the extreme price movements and showed that they do not react in the long-run to financial distress at PSE, while for the matured US market suggested a company/sector-specific reaction. We analysed behaviour of extreme price movements with respect to CDS. Our results suggested that both markets are different–extreme price movements at PSE are independent of CDS movements, while those at NYSE showed a sector/company specific reactions to CDS. In addition, recent crisis revived interest in financial transaction taxes (FTTs) as a means to offset negative risk externalities. However, up-to-date academic research does not provide sufficient insights into the effects of transaction taxes on financial markets, as the literature has here-to-fore been focused too narrowly on Gaussian variance as a measure of volatility. Therefore, we argued that it is imperative to understand the relationship between price jumps, Gaussian variance, and FTTs. While Gaussian variance is not necessarily problem in itself, the non-normality of return distribution caused by price jumps affects not only the performance of many risk-hedging algorithms but directly influences the frequency of catastrophic market events. To study the aforementioned relationship we used an agent-based model of financial markets. Its results showed that FTTs may increase the variance while decreasing the impact of price jumps. This result implies that regulators may face a trade-off between overall variance and price jumps when designing optimal tax.From the financial industry perspective, we have investigated trading opportunities of price jump clusters in the FX markets. We identified clusters for eight FX rates against the US dollar from 1-March-2013 to 6-June-2013 sampled at 5-minute frequency. We then proposed a high-frequency jump cluster-based trading strategy and showed that price jumps carry a tradable signal for all currencies; however, when incorporating the bid-ask spread, the only profitable currencies are the Euro, yen and, in some cases, rand. From the portfolio perspective, a combination of the Euro and yen represents a strategy robust to the holding period, minimizes the transaction costs, and diversifies out the US-related risk. This analysis suggests that the temporal market inefficiencies may arise in the FX markets due to the extensive hedging around the news announcements and price jumps serve as a suitable tool to identify such inefficiencies.ConclusionThis project extensively analysed the topic of price jumps in the high-frequency financial time series. We have shown that price jumps are significant component of the dynamics of all the analysed assets and addressed the issue from different perspectives ranging from regulatory perspective to trading floors and we have developed novel methods to achieve this.