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.
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.
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.
Upon successful completion of this module, students will have an understanding of:-
This module provides opportunities for the student to acquire or enhance the following skills: