MATHS 3012 - Financial Modelling: Tools & Techniques III

The growth of the range of financial products that are traded on financial markets or are available at other financial institutions, is a notable feature of the finance industry. A major factor contributing to this growth has been the development of sophisticated methods to price these products. The significance to the finance industry of developing a method for pricing options (financial derivatives) was recognized by the awarding of the Nobel Prize in Economics to Myron Scholes and Robert Merton in 1997. The mathematics upon which their method is built is stochastic calculus in continuous time. Binomial lattice type models provide another approach for pricing options. These models are formulated in discrete time and the examination of their structure and application in various financial settings takes place in a mathematical context that is less technically demanding than when time is continuous. This course discusses the binomial framework, shows how discrete-time models currently used in the financial industry are formulated within this framework and uses the models to compute prices and construct hedges to manage financial risk. Spreadsheets are used to facilitate computations where appropriate. Topics covered are: The no-arbitrage assumption for financial markets; no-arbitrage inequalities; formulation of the one-step binomial model; basic pricing formula; the Cox-Ross-Rubinstein (CRR) model; application to European style options, exchange rates and interest rates; formulation of the n-step binomial model; backward induction formula; forward induction formula; n-step CRR model; relationship to Black-Scholes; forward and future contracts; exotic options; path dependent options; implied volatility trees; implied binomial trees; interest rate models; hedging; real options; implementing the models using EXCEL spreadsheets.