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ST958 Advanced Topics in Mathematical Finance

Throughout the 2021-22 academic year, we will be adapting the way we teach and assess your modules in line with government guidance on social distancing and other protective measures in response to Coronavirus. Teaching will vary between online and on-campus delivery through the year, and you should read the additional information linked on the right hand side of this page for details of how this will work for this module. The contact hours shown in the module information below are superseded by the additional information. You can find out more about the University’s overall response to Coronavirus at: https://warwick.ac.uk/coronavirus.

All dates for assessments for Statistics modules, including coursework and examinations, can be found in the Statistics Assessment Handbook at http://go.warwick.ac.uk/STassessmenthandbook

ST958-15 Advanced Topics in Mathematical Finance

Academic year
21/22
Department
Statistics
Level
Taught Postgraduate Level
Module leader
David Hobson
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry
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

To provide an introduction to three advanced topics in Mathematical Finance.

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

Study time

Type Required
Lectures 27 sessions of 1 hour (18%)
Private study 123 hours (82%)
Total 150 hours
Private study description

Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.

Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Assessment group D1
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.

On-campus Examination 85%

The examination paper will contain a section of compulsory questions and a section of optional questions.


  • Answerbook Pink (12 page)
Assessment group R
Weighting Study time
Resit Examination 100%
Feedback on assessment
  • Verbal qualitative feedback will be given after class tests.
  • Written quantitative and qualitative feedback will be given after the final exam.
  • Solutions will be provided for the examination paper. Examination scripts are retained for external examiners and will not be returned to students.

Past exam papers for ST958

Courses

This module is Optional for:

  • USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
    • Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
    • Year 4 of G300 Mathematics, Operational Research, Statistics and Economics

This module is Option list A for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
  • Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
  • Year 5 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

This module is Option list D for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

This module is Option list E for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated