Course co-ordinator(s): Dr Timothy C Johnson (Edinburgh), Prof Gareth Peters (Edinburgh).
Aims:
This course introduces students to advanced topics in derivatives, developing on the material in the CT8 syllabus.
Summary:
This course developes the students understanding of derivatives by extending their comprehension of
- Stochastic Calculus applied to financial markets
- Exotic options and derivative portfolios
- Stochastic Volatility
- Numerical methods
- Modelling the Term Structure of Interest Rates
- Structured Derivatives and Synthetic Securities
This course covers some of the material in Subject ST6 of the Institute/Faculty of Actuaries examinations and, for the MSc in Actuarial Management, is synoptic with Derivative Markets (F71DM).
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Learning Outcomes: Subject Mastery
At the end of studying this course, students will understand
-
Ito calculus, Ito’s formula, statement of the Cameron-Martin-Girsanov Theorem, the concept of the Radon-Nikodym derivative, the Martingale Representation Theorem
-
Self-financing portfolios in continuous time and the construction of replicating strategies using the martingale approach
-
OU and Feller processes and derivation of BSM PDE
-
The role of the market price of risk in the transfer between the real-world and the risk-neutral probability measures
-
Hedging derivatives and the Greeks in continuous time models and to stuctures
-
Description of exotic options (including Quanto, Chooser, Barrier, Binary, Lookback Asian, Exchange, Basket options)
-
Management of derivative portfolios of using scenario analysis.
-
Risk management characteristics of certain exotic products
-
The role of the volatility parameter in the valuation of options
-
Estimation of volatility from market data
-
The “smile” effect and volatility surfaces
-
Finite differences and lattices
-
Trinomial trees
-
Monte Carlo techniques
-
Least-Squares (Longstaff-Schwartz) approach for Ameican options
-
The Black, Hull & White Vasicek and Cox-Ingersoll-Ross models (Ho & Lee, Black, Derman & Toy, Black & Karasinski)
-
HJM framework.
-
Libor Market Models
-
Implementation and calibration of models
-
Products for hedging non-financial risks
-
Securitisation
-
Credit risk
-
CDOs and CDSs
Reading list:
Due to the breadth of the material there is no specific recommended text, however as the course follows the ST6 syllabus students are advised to refer to the Core Reading for ST6 (supplied). The recommended reading for ST6 is:
- Hull, J., (2000) Options, futures and other derivative securities, Prentice Hall;
Assessment Methods: Due to covid, assessment methods for Academic Year 2020-21 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
SCQF Level: 10.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
VISION: further information and course materials are available on VISION