F71AP/F70DP Advanced Derivative Pricing

Dr Timothy C Johnson

Course co-ordinator(s): Dr Timothy C Johnson (Edinburgh).


This course introduces students to advanced topics in derivatives, developing on the material in the CT8 syllabus.

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisites: none.

Location: Edinburgh.

Semester: 2.


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).

Learning Outcomes: Subject Mastery

At the end of studying this course, students will understand

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: 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:


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:

2 hour end-of-year examination (80%), course work (20%).

SCQF Level: 10, 11.

Credits: 15.

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