Daniel J. Fenn

Limit Order Books

Limit order books (LOBs) match buyers and sellers in more than half of the worlds financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.

Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007-2008 credit crisis

We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We employ a node-centric approach that allows us to track the effects of the community evolution on the functional roles of individual nodes without having to track entire communities. As an example, we consider a foreign exchange market network in which each node represents an exchange rate and each edge represents a time-dependent correlation between the rates. We study the period 2005-2008, which includes the recent credit and liquidity crisis. Using community detection, we find that exchange rates that are strongly attached to their community are persistently grouped with the same set of rates, whereas exchange rates that are important for the transfer of information tend to be positioned on the edges of communities. Our analysis successfully uncovers major trading changes that occurred in the market during the credit crisis.

How does Europe Make Its Mind Up? Connections, cliques, and compatibility between countries in the Eurovision Song Contest

We investigate the complex relationships between countries in the Eurovision Song Contest, by recasting past voting data from 1992–2003 in terms of a dynamical network. Our analysis shows that the UK is remarkably compatible, or ‘in tune’, with other European countries during the period of study. Equally surprising is our finding that some other core countries, most notably France, are significantly ‘out of tune’ with the rest of Europe during the same period. In addition, our analysis enables us to confirm a widely-held belief that there are unofficial cliques of countries; however, these cliques are not always the expected ones, nor can their existence be explained solely on the grounds of geographical proximity. The complexity in this system emerges via the group ‘self-assessment’ process, and in the absence of any central controller. One might therefore speculate that such complexity is representative of many real-world situations in which groups of ‘agents’ establish their own inter-relationships and hence ultimately decide their own fate. Possible examples include groups of individuals, societies, political groups or even governments.

Temporal Evolution of Financial Market Correlations

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007-2008 credit and liquidity crisis.

Dynamical clustering of exchange rates

We use techniques from network science to study correlations in the foreign exchange (FX) market during the period 1991–2008. We consider an FX market network in which each node represents an exchange rate and each weighted edge represents a time-dependent correlation between the rates. To provide insights into the clustering of the exchange-rate time series, we investigate dynamic communities in the network. We show that there is a relationship between an exchange rates functional role within the market and its position within its community and use a node-centric community analysis to track the temporal dynamics of such roles. This reveals which exchange rates dominate the market at particular times and also identifies exchange rates that experienced significant changes in market role. We also use the community dynamics to uncover major structural changes that occurred in the FX market. Our techniques are general and will be similarly useful for investigating correlations in other markets.

THE MIRAGE OF TRIANGULAR ARBITRAGE IN THE SPOT FOREIGN EXCHANGE MARKET

We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with larger numbers of opportunities with shorter mean durations occurring during more liquid hours. We demonstrate further that the number of arbitrage opportunities has decreased in recent years, implying a corresponding increase in pricing efficiency. Using trading simulations, we show that a trader would need to beat other market participants to an unfeasibly large proportion of arbitrage prices to profit from triangular arbitrage over a prolonged period of time. Our results suggest that the foreign exchange market is internally self-consistent and provide a limited verification of market efficiency.

Self-organized global control of carbon emissions

There is much disagreement concerning how best to control global carbon emissions. We explore quantitatively how different control schemes affect the collective emission dynamics of a population of emitting entities. We uncover a complex trade-off which arises between average emissions (affecting the global climate), peak pollution levels (affecting citizens’ everyday health), industrial efficiency (affecting the nation’s economy), frequency of institutional intervention (affecting governmental costs), common information (affecting trading behavior) and market volatility (affecting financial stability). Our findings predict that a self-organized free-market approach at the level of a sector, state, country or continent can provide better control than a top-down regulated scheme in terms of market volatility and monthly pollution peaks. The control of volatility also has important implications for any future derivative carbon emissions market.

Relative Robust Portfolio Optimization with benchmark regret

We extend Relative Robust Portfolio Optimization models to allow portfolios to optimize their performance when considered relative to a set of benchmarks. We do this in a minimum volatility setting, where we model regret directly as the maximum difference between our volatility and that of a given benchmark. Portfolio managers are also given the option of computing regret as a proportion of the benchmark’s performance, which is more in line with market practice than other approaches suggested in the literature. Furthermore, we propose using regret as an extra constraint rather than as a brand new objective function, so practitioners can maintain their current framework. We also look into how such a triple optimization problem can be solved or at least approximated for a general class of objective functions and uncertainty and benchmark sets. Finally, we illustrate the benefits of this approach by examining its performance against other common methods in the literature in several equity markets.

Competitive carbon emission yields the possibility of global self-control

Abstract Despite many international climate meetings such as Copenhagen 2009, it is still unclear how annual global emissions can be reduced without requiring governments to micro-manage the emitting companies within their individual jurisdictions. Here we examine a simple, yet highly non-trivial, computer model of carbon emission which is consistent with recent activity in the European carbon markets. Our simulation results show that the ongoing daily competition to emit CO2 within a population of emitters, can lead to a form of collective self-control over the aggregated emissions. We identify regimes in which such a population spontaneously hits its emissions target with minimal fluctuations. We then focus on the emission dynamics induced by a governing body which chooses to actively manage the capping level. Finally we lay some formal stepping stones toward a complete analytic theory for carbon emissions fluctuations within this model framework – in so doing, we also connect this problem to more familiar theoretical terrain within computer science.