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Aims:

This module aims to introduce how financial markets based on limit order books operate, and their emerging non-trivial empirical regularities.ÌýWe will discuss the main empirical facts characterising modern financial markets, including intraday trading patterns, transaction costs, determinants of spread and quotes as well as the impact of orders’ execution. Part of the module will be devoted to the key modelling and theoretical approaches that are used to reproduce and ultimately understand the phenomena observed empirically.

Intended learning outcomes:

On successful completion of the module, a student will be able to:

1. Understand the mechanisms that underpin the functioning of financial markets based on limit order books.
2. Recognise and discuss the main empirical facts emerging in modern financial markets.
3. Understand and characterise the price impact of different types of orders and their execution.
4. Characterise the relationship between price impact, bid-ask spread, tick size, and liquidity.

Indicative content:

The following are indicative of the topics the module will typically cover:

Introduction to limit order markets:

• The module introduces the functioning and historical context of limit order-driven markets, including regulatory issues.

Empirical analysis of financial data:

• Analysis of the empirical facts characterising order driven financial markets. This includes, but it is not limited to, discussing typical behaviour of the distribution of returns, observing spread dynamics and intraday liquidity patterns.ÌýLimit order book data and price time series will be analysed to extract and understand typical stylised facts and common patterns across stocks and markets.

ÌýPrice impact:

• Analysis of order book events (market order submissions, limit order submissions, and cancellations) and their impact on market price. Different price impact empirical measures will be introduced, as well as the theoretical framework to model price impact and use it in the design of optimal execution strategies.

Theoretical modelling approaches:

• An overview of different modelling approaches to characterise traders’ behaviour, trades submission and their aggregate effect on price and liquidity dynamics. We will discuss for example zero-intelligence models characterising limit order book dynamics to investigate the implications for price impact and the effect on spread and liquidity.

Requisites:

To be eligible to select this module as optional or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; and (2) have a good background in mathematics and probability; and (3) have some programming experience (e.g., in Python).