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.
Prerequisites:
Students on the MSc in Mathematical Finance: ST908: Stochastic Calculus for Finance
Students on Integrated Masters courses in Statistics*: ST401 Stochastic Methods in Finance
To provide an introduction to three advanced topics in Mathematical Finance.
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 nonlinear 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; highfrequency 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 eventdriven times. Agentbased models, microstructure of the double auction, zerointelligence, econophysics approaches via reactiondiffusion and decompositionevaporation processes. Markov models of LOB, diffusive limits, largescale limits, queueing theory modelling, Hawkes processes, SDEs and PDEs modelling, gametheoretic modelling.
By the end of the module, students should be able to:
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), 236249.
Collin‐Dufresne, P., Goldstein, R., and Hugonnier, J. (2004): A general formula for valuing defaultable securities, Econometrica 72(5), 13771407.
Gatheral, J. (2006): The volatility surface: a practitioner’s guide, Wiley.
TBC
TBC
Type  Required 

Lectures  27 sessions of 1 hour (18%) 
Private study  123 hours (82%) 
Total  150 hours 
Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Weighting  Study time  

Class Test 1  5%  
The class test will take place during a lecture in week 4 of term 2. 

Class Test 3  5%  
The class test will take place during a lecture in week 10 of term 2. 

Class Test 2  5%  
The class test will take place during a lecture in week 7 of term 2. 

Oncampus Examination  85%  
The examination paper will contain a section of compulsory questions and a section of optional questions.

Weighting  Study time  

Resit Examination  100% 
This module is Optional for:
This module is Option list A for:
This module is Option list D for:
This module is Option list E for: