ST401 Stochastic Methods in Finance
Please note that all lectures for Statistics modules taught in the 2022-23 academic year will be delivered on campus, and that the information below relates only to the hybrid teaching methods utilised in 2021-22 as a response to Coronavirus. We will update the Additional Information (linked on the right side of this page) prior to the start of the 2022/23 academic year.
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 The contact hours shown in the module information below are superseded by the additional information.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
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 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 | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination | 100% | No | |
|
Answer all questions.
|
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Assessment group R
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
|
Answer all questions. ~Platforms - Moodle
|
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Feedback on assessment
Solutions and cohort level feedback will be provided for the examination.
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