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Options, Futures & Other Derivative Securities - FIN9007

The aim of this module is to develop in students a theoretical and practical knowledge of derivative instruments.

This module provides participants with an exhaustive coverage of widely used derivative products stressing pricing and uses for financial engineering and risk management.  The module provides an overview of derivative instruments, markets, participants and uses.  It focuses on the pricing and uses of futures, forwards and options. 

The cost of carry relationship, the binomial approach, the Black-Scholes model and its variants are detailed to equip participants with the basic tools for pricing derivatives.  The module examines practical uses of derivative securities as risk management tools for corporations and financial institutions.

Areas to be covered include:

THE MOVEMENT OF FUTURES PRICES: The distributional characteristics of futures prices. Are futures price changes stable paretian or a mixture of normal distributions or exponential generalised beta or the skewed generalised t-distribution?

MEAN VARIANCE APPROACHES TO HEDGE RATIO DETERMINATION, STOCK INDEX FUTURES AND HEDGING EFFECTIVENESS: The mean-variance approach to hedge ratio construction. Hedging with stock index futures. Hedging effectiveness and hedge ratio estimation - OLS, ECM and GARCH procedures. Duration and Expiration effects.

THE STOCHASTIC PROCESS OF ASSET PRICES AND THE DERIVATION OF THE BLACK-SCHOLES MODEL:The Wiener process and rare events in financial markets; Ito processes; Ito's lemma; generalised Ito's lemma; Black-Scholes differential equation; Black-Scholes pricing formula; options on stocks paying known dividends;  pseudo-American model;  option on stock indices, currency options and options on futures;

VOLATILITY: Estimating volatility: historical; implied - application of Newton-Raphson. Empirical characteristics of volatility: smiles; term structure skew; mean reversion; Forecasting volatility: application of GARCH; empirical evidence of volatility forecasts - implied versus historical; Bisection.

EXOTIC OPTIONS: Types of exotic options - barrier options; lookback options; strike options; binary or digital options; compound options; and chooser options.

INTEREST RATE DERIVATIVES: The standard market models; models of short rate; HJM and LMM models.

RISK AND REGULATION WITH EMPHASIS ON VALUE AT RISK: Regulation of Financial Institutions; value at risk and forecast accuracy; capital adequacy and value at risk; value at risk and the variance covariance approach; value at risk and non-parametric methods such as historical simulation and bootstrapping; value at risk and linear and non-linear positions.

CREDIT RISK AND CREDIT DERIVATIVES: Default probabilities;  Recovery rates;  Default correlation;  Credit default swaps;  Asset-backed securities.

REAL OPTIONS: The option to expand, contract, default, abandon and switch. The valuation of real options in the face of compoundness, interaction between options and ownership. Real options and the valuation of internet companies.

Contact hours

2 x 2 hour lectures per week for 8 weeks during the 2nd semester.

Essays - 1

Group Excercise - 1


This module will be assessed by a final written examination (60%) and a continuous assessment element (40%) which will be made up of an extended essay and a group assignment.

Indicative reading

Hull, John (2009), Options, Futures and Other Derivatives, (7th Ed), Prentice Hall.

Cuthbertson, Keith and Nitzsche, Dirke (2001), Financial Engineering: Derivatives and Risk Management, John Wiley & Sons.

Hull, John  (2007), Risk Management and Financial Institutions, Prentice Hall. 

Learning outcomes

Upon successful completion of this module, students will have an understanding of:-

  • how to assess the distributional properties of futures contracts
  • how to construct hedges using futures
  • the concept of stochastic processes
  • how to derive the Black-Scholes model from first principles
  • the techniques employed to estimate volatility
  • the use of binomial and trinomial models in pricing options
  • the use of Monte-Carlo simulation in pricing options
  • the pricing and use of a selection of exotic options
  • interest rate derivatives, credit risk, and credit derivatives
  • risk assessment in the context of derivative markets

Acquisition of Skills

This module provides opportunities for the student to acquire or enhance the following skills:

Subject-specific Skills

  • The  ability to construct arguments and exercise  problem solving skills in the context  of theories of finance and risk management
  • The  ability to use computer-based mathematical  / statistical / econometric packages to  analyse and evaluate relevant data
  • The  ability to read and evaluate finance and  risk-related academic literature
  • The  ability to appreciate, construct and analyse  mathematical, statistical, financial and economic  models of practical risk situations
  • The  ability to connect business problems with  risk management
  • The  ability to marry regulatory structure with  the principles of risk sharing and risk  mitigation

Cognitive Skills

  • Problem  solving
  • Logical  reasoning
  • Independent  enquiry
  • Critical  evaluation and interpretation
  • Self  assessment and reflection

Transferable Skills

  • The  ability to synthesise information/data from  a variety of sources including from databases,  books, journal articles and the internet
  • The  preparation and communication of ideas in  finance, information economics  and risk management  in both written and presentational forms
  • The  ability to work both independently and  in groups
  • Organisation  and time management
  • Problem  solving and critical analysis
  • Work-based  skills; use of IT, including word-processing,  email, internet and statistical/econometric/risk  management packages
  • The  ability to communicate quantitative and qualitative  information together with analysis, argument  and commentary in a form appropriate to  different intended audiences