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

Aims:

The purpose of this module is to introduce students to advanced and practical topics in derivative markets, which are essential preparation for a career in the financial industry.

## Detailed Information

Pre-requisite course(s): F79DF Derivative Markets and Discrete-time Finance & F79SP Stochastic Processes .

Linked course(s): F70CF Continuous-Time Finance .

Location: Edinburgh.

Semester: 2.

Syllabus:

• American options
• Numerical methods for pricing American options
• Exotic options; different types
• Methods for pricing exotic options
• Interest-rate models: Black’s formula, short-rate models; market models

• Pricing caplets and swaptions
• Review of Black-Scholes assumptions and their validity in the real world
• Reasons for market incompleteness and implications
• Market price of risk
• Examples of market incompleteness

Learning Outcomes: Subject Mastery

On completion of the course the student should be able to:
• Describe the difference between an exchange-traded and an over-the-counter (OTC) derivative, and describe the advantages and disadvantages of each;
• Be able to classify exotic options according to their path dependency, time dependence, order, dimensionality and decision structure;
• Demonstrate a knowledge of the Girsanov Theorem and how it is used in the change of probability measure;
• Calculate the price of a vanilla barrier option and a simple lookback option, and calculate their Greeks;
• Demonstrate a knowledge of the different methods that can be used to price American options including the Longstaff-Schwartz least-squares Monte-Carlo approach;
• Describe and apply the Longstaff-Schwartz least-squares Monte-Carlo approach for pricing an American option;
• Describe and apply appropriate numerical methods for pricing other exotic options including Asian options and basket options;
• Demonstrate a knowledge of the different frameworks that can be used to describe the dynamics of the term structure of interest rates;
• Show how the Hull-White model can be used to generalise the Vasicek model and how it can be implemented
• Describe and apply Black’s formula for pricing interest-rate derivatives
• Show how to value interest-rate derivatives using a change of measure to the forward measure
• Describe and apply the LIBOR market model for pricing caplets and other derivatives
• Describe and apply the swaps market model for pricing swaptions
• Discuss the role of model risk in interest-rate modelling
• Discuss the accuracy of the individual assumptions underpinning the Black-Scholes model and show the failure of individual assumptions leads to market incompleteness
• Discuss how market incompleteness arises in a variety of models
• Explain why market incompleteness means there might not be a unique risk-neutral price for a derivative
• Explain how to use market information to extract a market price of risk
• Show how the market price of risk can be used to calculate market-consistent prices for new contracts

Learning Outcomes: Personal Abilities

• Demonstrate the ability to learn independently and as part of a group
• Present results in a way that demonstrates that they have understood the technical and broader issues of advanced interest-rate modelling and derivative pricing.

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;

SCQF Level: 10.

Credits: 15.

## Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.

Canvas: further information and course materials are available on Canvas