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.)
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.
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.
By the end of the module, students should be able to:
View reading list on Talis Aspire
TBC
TBC
| 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 |
Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for class tests and the examination.
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.
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination | 100% | No | |
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Answer all questions.
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| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
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Answer all questions. ~Platforms - Moodle
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Solutions and cohort level feedback will be provided for the examination.
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: