• financial market
• quantitative finance
• econophysics
• Hawkes processes

This thesis deals with an interesting problem in the field of econophysics: stochastic modelling of the arrival process of market events in continuous time. In this context, a market event is any type of event registered on the market at a definite time, for example the occurrence of a transaction or a change in the price of an asset. This is a topic of interest both for the academia and for the financial industry, as a faithful description of the time properties of events arrivals is essential for a complete understanding of the market and has important consequence for the construction of trading strategies ad for the management of risk.

The research work we present was conduced in collaboration with the eFX Quantitative Trading group of HSBC in London. They provided us with Foreign Exchange (FOREX) market data and invaluable insight into the market structure and mechanisms.

Market activity, intended as the number of events per unit time, is not a time homo- geneous process. Instead, events tend to cluster in time. Its dynamics is influenced both by endogenous and exogenous events. Traders react to other market participants activity and the price movement they generate: intense activity triggers more activity in a self-exciting fashion. Also exogenous shocks play a relevant role, for example when a news is announced, market activity can have a sudden increase. We aim at describe these two mechanisms under the same dynamic model and investigate their relative contribution to market activity.

The mathematical description of this phenomenon comes from the theory of point processes: the sequence of times corresponding to market events is viewed as the realization of a point process on the real line. Hawkes self-exciting point processes are a promising tool to model this phenomenon, since they are characterized by this cluster structure. They were originally introduced in the field of seismology by Hawkes (1971) to describe the aftershocks that follow a major earthquake. They subsequently gained a certain popularity in many other fields including high frequency finance. Basically, Hawkes processes are Poisson processes with a time dependent intensity. Their self-exciting nature derives from the fact that the intensity depends on the past history of the process and has a jump every time an event is generated, leading to "cascades" of events. The way past events influence the intensity is regulated by the functional form of the so-called kernel of the process.

The original research work we present in this thesis consists of three parts. First we analyse in detail the properties of our equity and FOREX datasets. The equity dataset is relative to trades on the Apple stock at NASDAQ electronic market in August and September 2009. The FOREX dataset is constituted of bid-ask data concerning three currencies pairs, namely EUR/USD, EUR/JPY, USD/JPY, from the interbank trading platform EBS live.

In the second part we fit a Hawkes process with different specifications for the kernel on both equity and FOREX data. In this part we focus mainly on the endogenously- generated activity, which, as it turns out, is the main driver of market activity itself. We evaluate goodness-of-fit for different choices of the process kernel. We discuss the strength and limits of the models on both markets and we compare our results with those already published in the literature. We find also that FX market operate close to a critical state, as recently observed in other markets.

Finally, we develop an extension of the Hawkes model that takes into account also the effects of macroeconomic news announcements on FOREX market activity. These kind of announcements are the main exogenous shocks on the FOREX market. In fact, the value of a currency against another one is tightly linked to the market perception of the relative strengths of the respective economies and to the decisions of the respective central banks. Hence, a shift in market perception caused by an unexpected news from the economy can lead to frenetic activity on the market after the announcement. In these cases simple Hawkes models like the ones applied in the second part fail to reproduce the sudden increase in market activity that is observed. On the contrary, our extension captures very well the way news affects market activity, also with regard to the extent the news matched market expectations.