Introductory description

Three topics will be covered each year, motivated by current questions relevant to the financial industry. Each topic will be presented by a different lecturer, who is an expert in the research area.

This module is available for students on a course where it is a listed option (subject to restrictions*) and as an Unusual Option to students who have completed the prerequisite modules.

Pre-requisites:
Students on the MSc in Mathematical Finance: ST908: Stochastic Calculus for Finance
Students on Integrated Masters courses in Statistics*: ST401 Stochastic Methods in Finance

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Three topics will be covered each year, motivated by current questions relevant to the financial industry. Example topics are algorithmic trading, introduction to market microstructures, limit order books.

Algorithmic trading would cover topics such as electronic markets - market participants, order types, and the limit order book. Stochastic optimal control and stopping; the dynamic programming principle and HUB equation. Optimal execution models with temporary and permanent price impact, linear and non-linear impact. Optimal execution models with limit orders and market orders; fill probabilities. Market Making. Targeting volume, for example, VWAP schedules.

Introduction to market microstructures would cover topics such as: order flow and liquidity; inventory risk, trade size and market depth; measuring liquidity and price discovery; static limit order markets; dynamic limit order markets; high-frequency trading; trading strategies.

Limit order books would cover topics such as main statistical characteristics of LOB: the distribution of the time of arrivals, volumes, placement and cancellation of orders, the shape of LOB and the intraday seasonality, modelling in physical time and event-driven times. Agent-based models, microstructure of the double auction, zero-intelligence, econophysics approaches via reaction-diffusion and decomposition-evaporation processes. Markov models of LOB, diffusive limits, large-scale limits, queueing theory modelling, Hawkes processes, SDEs and PDEs modelling, game-theoretic modelling.

Learning outcomes

By the end of the module, students should be able to:

• Compute and explain key variables in the relevant models.
• Apply appropriate mathematical techniques.
• Analyse and compare different modelling approaches.

Indicative reading list

Föllmer, H. and Schied, A. (2016): Stochastic Finance, 4th ed., de Gruyer.
McNeil, A., Frey, R. and Embrechts, P. (2015): Quantitative Risk Management, 2nd rev. ed., Princeton University Press.
Eisenberg, L., and Noe, T.H. (2001): Systemic risk in financial systems, Management Science 47(2), 236-249.
Collin‐Dufresne, P., Goldstein, R., and Hugonnier, J. (2004): A general formula for valuing defaultable securities, Econometrica 72(5), 1377-1407.
Gatheral, J. (2006): The volatility surface: a practitioner’s guide, Wiley.

Subject specific skills

TBC

Transferable skills

TBC