Financial Statistics 4 STATS4010

  • Academic Session: 2018-19
  • School: School of Mathematics and Statistics
  • Credits: 10
  • Level: Level 4 (SCQF level 10)
  • Typically Offered: Semester 2
  • Available to Visiting Students: Yes
  • Available to Erasmus Students: Yes

Short Description

To provide an appreciation of the uses of mathematics and statistics in finance and insurance; To provide details of some statistical methods used in finance;  To describe applications of mathematical, optimisation and probabilistic methods from other courses;  To provide an introduction to the ideas of derivative pricing, portfolio management and life insurance.

Timetable

20 lectures ( 2 each week)

5 tutorials (fornightly)

Requirements of Entry

The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Statistics and/or Mathematics.

Excluded Courses

STATS5053 Financial Statistics (Level M)

Assessment

End-of-Course Examination 100%

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

Course Aims

To provide an appreciation of the uses of mathematics and statistics in finance and insurance;
To provide details of some statistical methods used in finance;
To describe applications of mathematical, optimisation and probabilistic methods from other courses;
To provide an introduction to the ideas of derivative pricing, portfolio management and life insurance.

Intended Learning Outcomes of Course

By the end of this course students will be able:

■ to explain the relationships between continuously accumulated and periodically paid interest rates;

■ to explain the idea and terminology of futures contracts (long, short positions, hedging, arbitrage);

■ to describe the optimal hedge ratio and hedging using futures;

■ to calculate futures prices for non-dividend paying stock, and for dividend paying stock with continuous and periodic dividends;

■ to explain bond prices, the concept of coupons and discounting;

■ to describe the basic terminology for options ( call, put, American, European);

■ to draw and explain profit/loss graphs for options;

■ to explain about spreads and combinations (bull, bear, butterfly, straddle and strangle);

■ to derive inequalities for European and American calls and puts;

■ to describe put-call parity for European and American options;

■ to explain the pricing of American calls;

■ to calculate option values on one-step binomial trees;

■ to implement the risk-neutral approach to the calculation of probabilities of up-movements;

■ to carry out calculations on two-step binomial trees for option pricing of European and American options by working backwards;

■ to describe hedging for option writers, including delta hedging;

■ to explain the basic concepts of stochastic processes on binomial trees (stochastic processes, measure, filtration, claim, conditional expectation, previsible processes, martingales);

■ to explain the idea of self-financing hedging strategies;

■ to describe the stock process processes, geometric Brownian motion, and how to calculate the distribution of the stock price that follows a geometric Brownian motion if the return and the volatility are given, as well as the probability that a particular European option will be exercised;

■ to state and be able to implement Ito's formula;

■ to describe the application of change of measure and martingale representation theorem to option pricing;

■ to describe the Black-Scholes model, and be able to calculate the pricing of European calls and puts, implied volatilities, and the pricing of options on foreign exchange and dividend-paying stocks;

■ to explain the mean-variance approach (for two-asset portfolios);

■ to demonstrate the graphical meaning of a capital market line;

Minimum Requirement for Award of Credits

N/A