# Derivatives

Module Code:
C333

#### Introduction

The expansion of financial markets since 1973 has been founded on the growth of derivatives. This was made possible by the development of models for valuing derivatives based upon the mathematics of financial calculus. In this module you will learn the application of those principles to the valuation of derivatives.

#### Resources

###### Study Guide

You will receive a looseleaf binder containing eight units. The units are carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the further assigned readings. The unit files are also available to download from the Virtual Learning Environment.

###### Textbook

Hull, John C. (2011) Options, Futures, and Other Derivatives, 8th Edition, Pearson Education.

This is a classic textbook on derivatives, written by an authority in the field and covers both theoretical and practical aspects in the use of derivatives. This edition also explains a number of recent events and analyses relevant case studies in financial markets.

The textbook by Hull comes with access to the proprietary software DerivaGem. This software enables you to compute the prices of a large number of derivatives and to draw the relevant graphs.

###### Virtual Learning Environment

You will have access to the VLE, which is a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

#### Objectives and learning outcomes of the module

By the end of this course you will be able to:

• Apply the principles of hedging and dynamic hedging;
• Understand the Black-Scholes model and its applications:
• Calculate delta and other measures of sensitivity;
• Evaluate interest rate swap contracts;
• Discuss the role of credit derivatives in risk management;
• Apply appropriate numerical methods for analysing derivatives.

#### Scope and syllabus

###### Unit 1: Derivatives Contracts
• 1.1 Introduction
• 1.2 Forward Contracts
• 1.3 Futures Contracts
• 1.5 A 'Health Warning'
• 1.6 Conclusions
###### Unit 2: Properties of Stock Options
• 2.1 Options
• 2.2 Stock Options
• 2.3 Warrants, Employee Stock Options and Convertibles
• 2.4 Basics of Pricing Stock Options
• 2.5 Trading Strategies Involving Options
• 2.6 Conclusions
###### Unit 3: The Behaviour of the Stock Price and the Black-Scholes model
• 3.1 Introduction
• 3.2 The Wiener Process
• 3.3 The Behaviour of Stock Prices
• 3.4 Itô's Lemma
• 3.5 The Lognormal Property of Stock Prices
• 3.6 The Black-Scholes-Merton Equation and the Black-Scholes Formula
• 3.7 Conclusions
###### Unit 4: Greek Letters and Trading Strategies
• 4.1 Naked and Covered Positions
• 4.2 Delta Δ Hedging
• 4.3 Theta Θ
• 4.4 Gamma Γ
• 4.5 Vega v
• 4.6 Rho ρ
• 4.7 Hedging and Portfolio Insurance
• 4.8 Conclusions
###### Unit 5: Interest Rate Models
• 5.1 Interest Rates
• 5.2 Forward Rates
• 5.3 Management of Bond Portfolios
• 5.4 Swaps
• 5.5 Currency Swaps
• 5.6 Bond Options
• 5.7 Conclusions
###### Unit 6: Credit Derivatives and Credit Risk
• 6.1 Credit Ratings and Default Probabilities
• 6.2 Mitigation of Credit Risk and Default Correlation
• 6.3 Credit Default Swaps
• 6.4 Asset-Backed Securities and Collateralized Debt Obligations
• 6.5 Correlation and the Gaussian Copula
• 6.6 Conclusions
###### Unit 7: Some Exotic Options
• 7.1 Exotic Options
• 7.2 Barrier, Binary, and Lookback Options
• 7.3 Asian Options
• 7.4 Some Other Exotic Options
• 7.5 Weather and Energy Derivatives
• 7.6 Insurance Derivatives
• 7.7 Conclusions
###### Unit 8: Further Numerical Procedures
• 8.1 Binominal Trees
• 8.2 Alternative Procedures for Constructing Trees
• 8.3 Monte Carlo Simulations
• 8.4 Finite Difference Methods
• 8.5 Alternatives to Black-Scholes
• 8.6 Stochastic Volatility Models
• 8.7 American Options
• 8.8 Conclusions

#### Method of assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 5, and the second assignment at the end of the module, on the Tuesday after Week 8. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in April each year.

### Disclaimer

Important notice regarding changes to programmes and modules