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ST401 Stochastic Methods in 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 The contact hours shown in the module information below are superseded by the additional information.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

ST401-15 Stochastic Methods in Finance

Academic year
21/22
Department
Statistics
Level
Undergraduate Level 4
Module leader
Gechun Liang
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry
Introductory description

This module runs in Term 1 and is only available to students in their final year of an integrated masters in the Department of Statistics. It is not available as an Unusual Option.

Pre-requisites: ST318 Probability Theory and ST339 Introduction to Mathematical Finance.

Leads To: ST909 Continuous Time Finance for Interest Rate Models.

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries module CM2. (Independent application with the IFoA may be required to receive the exemption.)

Module web page

Module aims

To provide an introduction to continuous time stochastic models as applied in mathematical finance. To cover, in conjunction with parts of the Institute and Faculty of Actuaries syllabus. To gain an understanding of Brownian Motion and Stochastic Calculus. To be able to use this to model the evolution of financial markets in continuous time and price a variety of financial instruments.

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.

Content:
Introduction to Brownian Motion and Stochastic Calculus.
Introduction to SDEs (Stochastic Differential Equations) and Markov processes.
Continuous-time models of security prices.
Risk-neutral evaluation and equivalent martingale measures, Girsanov and martingale representation theorems.
Black-Scholes theory: PDE and SDE approaches.
Basic Greeks, delta-hedging.
Put-Call parity and Put-Call symmetry.
Introduction to optimal stopping and American Options.
Bond prices and term structure of interest rates: Hull-White, Vasicek and CIR models.

Learning outcomes

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

  • Know how probability models are used in financial mathematics
  • Understand the concept of Brownian motion
Indicative reading list

View reading list on Talis Aspire

Subject specific skills

TBC

Transferable skills

TBC

Study time

Type Required Optional
Lectures 30 sessions of 1 hour (20%) 2 sessions of 1 hour
Tutorials 5 sessions of 1 hour (3%)
Private study 115 hours (77%)
Total 150 hours
Private study description

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

Costs

No further costs have been identified for this module.

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

Students can register for this module without taking any assessment.

Assessment group B1
Weighting Study time
On-campus Examination 100%

Answer all questions.

~Platforms - Moodle


  • Answerbook Pink (12 page)
  • Graph paper
Assessment group R
Weighting Study time
Online Examination 100%

Answer all questions.

~Platforms - Moodle


  • Graph paper
Feedback on assessment

Solutions and cohort level feedback will be provided for the examination.

Past exam papers for ST401

Courses

This module is Optional for:

  • Year 1 of TMAA-G1PE Master of Advanced Study in Mathematical Sciences
  • 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