Financial Mathematics

(2-4 Credit Hours) · Undergraduate

University of Sydney: MATH 3075 - This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and hedging of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Lectures in the mainstream unit are held concurrently with those of the corresponding advanced unit. MST 30030 Financial Mathematics at UCD; The aim of "Financial Mathematics" is to introduce to the student to the Black-Scholes model for pricing options. The module opens by looking at various types of options and discussing their properties. The technique of constructing binomial trees to price options (based on the Cox, Ross and Rubenstein paper of 1979) is then discussed in detail. We then study the model of stock price behaviour introduced by Black, Scholes and Merton in 1973, and derive the Black-Scholes model for valuing European call and put options on a non-dividend-paying stock. A brief introduction to probability theory is included in the course.