MATH5965 is a Mathematics Level V course. See the course overview below.

Units of credit: 6

Prerequisites:

Cycle of offering: yearly in Semester 1.

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. (This pdf will usually be updated by the end of the first week of the semester.)

The Online Handbook entry contains up-to-date timetabling information.

The course provides an overview of the most important classes of financial contracts that are traded either on exchanges or over-the-counter between financial institutions and their clients. In particular, we discuss options of European and American style, futures contracts and forward contracts.

The basic ideas of arbitrage pricing within the set-up of a one-period model are introduced. In the next step, we analyse the valuation and hedging of European and American options and general contingent claims in the framework of the classic Cox-Ross-Rubinstein (CRR) binomial model of the stock price. We also show how to derive the famous Black-Scholes options pricing formula as the limit of CRR prices.

Finally, a general theory of arbitrage-free discrete-time models of spot and futures markets is presented. In particular, we prove the so-called fundamental theorems of asset pricing (FTAP) for finite models of security markets. The first FTAP establishes the equivalence between the no-arbitrage property of a security market model and the existence of a martingale measure. The second FTAP shows that the model completeness can be characterised in terms of the uniqueness of a martingale measure. These two results furnish a theoretical underpinnig of the modern theory of derivatives pricing in stochastic models of security markets.

The course is a prerequisite for MATH5816 Continuous Time Financial Modelling.