Course co-ordinator(s): Dr Timothy C Johnson (Edinburgh).
Aims:
The aims of this course are:
• To provide a thorough grounding in advanced topics of derivative markets
• To introduce mathematical concepts related continuous time martingales processes
• To provide students with a good understanding of developing the BSM model to different asset price models, including dividends and stochastic volatility
• To provide students with a good understanding of pricing American options
• To provide students with a good understanding of exotic options
• To introduce the student to numerical methods for pricing
• To provide students with a good understanding of modelling( the term structure of) interest rates
• To introduce the student to securitisation and credit derivatives
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Linked course(s): F71DV Derivatives Markets and Pricing .
Location: Edinburgh, Malaysia.
Semester: 2.
Syllabus:
Stochastic Calculus applied to financial markets
• 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
Exotic options and derivative portfolios
• 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 Stochastic Volatility
• The role of the volatility parameter in the valuation of options
• Estimation of volatility from market data
• The “smile” effect and volatility surfaces Numerical methods
• Finite differences and lattices
• Trinomial trees
• Monte Carlo techniques
• Least-Squares (Longstaff-Schwartz) approach for Ameican options Modelling the Term Structure of Interest Rates
• 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 Structured Derivatives and Synthetic Securities
• Products for hedging non-financial risks
• Securitisation
• Credit risk
• CDOs and CDSs
Learning Outcomes: Subject Mastery
The aims of this course are:
• To provide a thorough grounding in advanced topics of derivative markets
• To introduce mathematical concepts related continuous time martingales processes
• To provide students with a good understanding of developing the BSM model to different asset price models, including dividends and stochastic volatility
• To provide students with a good understanding of pricing American options
• To provide students with a good understanding of exotic options
• To introduce the student to numerical methods for pricing
• To provide students with a good understanding of modelling( the term structure of) interest rates
• To introduce the student to securitisation and credit derivatives
Learning Outcomes: Personal Abilities
• Show an appreciation of the interface between academic theory and industrial practice
• Demonstrate the ability to learn independently and as part of a group
• Demonstrate knowledge of computational issues
• Manage time, work to deadlines and prioritise workloads
• Present results in a way that demonstrates that they have understood the technical and broader issues of
derivative pricing
• Show an appreciation of the role of derivative markets in the management of a variety of risks
Reading list:
Reading
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 2021-22 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: 11.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
Canvas: further information and course materials are available on Canvas