Aims

To develop a knowledge and understanding of some commonly used financial models in the analysis of financial data.

To gain an understanding of the principles and the practical applications of Bayesian Statistics to more complex models relevant to practical data analysis. To improve data-analytic and report-writing skills.

Module summary
The demand for mathematical skills in financial institutions has increased considerably over the recent past. Financial analysts use sophisticated stochastic models to describe the unpredictable behaviour of markets, derive computable pricing methods and analyse financial data. The course deals with commonly used models for stock prices of risky assets and methods for pricing financial derivatives, such as options and contingent claims. The analysis of such models requires knowledge from probability, stochastic processes and statistics.

The course also builds on the foundations of Bayesian inference laid in MAS2903. We consider extensions to models with more than a single parameter and how these can be used to analyse data. We also provide an introduction to modern computational tools for the analysis of more complex models for real data.

Outline Of Syllabus

Risk-free money market. Financial derivatives: call and put options of European type, contingent claims, other exotic options, arbitrage. Continuous-time models of stock price: Brownian/Geometric Brownian motion, Black-Scholes pricing. Volatility estimation using historic data, implied volatility. Monte Carlo pricing. Itô calculus: Itô integral and Itô formula. Models of interest rate as stochastic differential equations. Use of R for calculation and simulation.

Review of Bayesian inference for single parameter models. Inference for multi-parameter models using conjugate prior distributions: mean and variance of a normal random sample. Asymptotic posterior distribution for multi-parameter models. Introduction to Markov chain Monte Carlo methods: Gibbs sampling, Metropolis-Hastings sampling, mixing and convergence. Application to random sample models using conjugate and non-conjugate prior distributions. Computation using R.

Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Rationale And Relationship

A substantial formal examination is appropriate for the assessment of the material in this module. The course assessments will allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.