Learning Outcomes:
On successful completion of this module, the student is expected to be able to understand the definitions, theorems and examples covered in all of the topics listed above, and carry out associated computations.
Curricular information is subject to change.
The aim of this module is to apply the methods of stochastic calculus to no-arbitrage theory, interest-rate modelling, equity, inflation and applications to pricing. Topics include: a review of Black-Scholes option pricing and the change of measure technique; bonds and interest rates (bank account and short rates, zero coupon bonds and interest rate curves, coupon bonds, swap and yields, yield and duration); multi-dimensional Itô calculus (review of 1-dimensional case, multi-dimensional Itô formulae, correlated Wiener processes); martingale models for the short rate (one- and two-factor short-rate models, classical time-homogeneous short rate models e.g. Vasicek and Dothan models, Hull-White extended Vasicek model, two-additive-factor Gaussian model G2++); forward rate models and market models (forward rate models e.g. Heath-Jarrow-Morton framework, market models e.g. the LIBOR market model); main equity models (Heston, Variance gamma); jarrow-Yildirim inflation model.
About this Module
Student Effort Hours:
| Student Effort Type | Hours |
|---|---|
| Lectures | 48 |
| Tutorial | 12 |
| Autonomous Student Learning | 160 |
| Total | 220 |
Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.Requirements, Exclusions and Recommendations
Learning Requirements:It is necessary for the student to have taken MATH40430 and ACM30080 (or equivalent) in order to take this module. It is also necessary for the student to have taken MATH40690.
Module Requisites and Incompatibles
Incompatibles:MATH40770 - Adv Financial Models (online)
| Resit In | Terminal Exam |
|---|---|
| Summer | Yes - 2 Hour |
Feedback Strategy/Strategies
• Group/class feedback, post-assessment
How will my Feedback be Delivered?
Not yet recorded.
T. Björk, Arbitrage Theory in Continuous Time, Oxford University Press 2005.
D. Brigo, F. Mercurio, Interest Rate Models - Theory and Practice (Second Ed.), Springer Verlag 2006.
D. Brigo, F. Mercurio, Interest Rate Models - Theory and Practice (Second Ed.), Springer Verlag 2006.