Mathematics BSc (Hons)

Module CG0010 - Financial Mathematics

(20.00 Credits)

SYNOPSIS OF MODULE Financial mathematics brings together mathematics, computing and statistics to problems arising in the fast-developing financial industry. This module provides an introduction to concepts in financial mathematics and methods of modelling and analysis of financial products. Assessment is by a combination of formal examination and in-course assignment.


INDICATIVE READING LIST OR OTHER LEARNING RESOURCES Hardy, M et al Core Reading 2001, Subject 102 ;Financial Mathematics, Instititute of Actuaries. McCutcheon, J.J. and Scott, W.F. (1986), An Introduction to the Mathematics of Finance, Butterworth-Henemann. Ross, S.M. (1999) An Introduction to Mathematical Finance, CUP. Institute of Actuaries (1980) Formulae and Tables for Actuarial Examinations, Institute of Actuaries.


OUTLINE SYLLABUS Interest: Simple and compound interest. Effective and nominal interest rates. Force of interest. Interest paid monthly. Present values. Cash flows and equations of value. (10%) Annuities: Annuities with annual payments, and payments more regularly. Payments in arrear and in advance. Deferred and varying annuities, annuities payable continuously. Loans, loan structure and equal payments. (15%). Discounted cash flow: Generalised cash flow model. Project appraisal at fixed interest rates. Comparison of two investment projects. Different interest rates for lending and borrowing. Payback periods. Measurement of investment performance. (15%) Investments: Types of investments. Valuation of fixed interest securities and uncertain income securities. Real rates of interest. Effects of inflation. Capital gains tax. (20%) Arbitrage in financial mathematics: Forward contracts. Calculating delivery price and delivery value of forward contracts using arbitrage-free pricing methods. Discrete and continuous time rates. (15%). Life Insurance: Term insurance and whole life insurance. Curtate future lifetime. Life tables, expectation of life. Annual and monthly premium. Endowments. Payment at death. (15%). Stochastic Interest Rates: Varying interest rates. Independent rates of return. Expected values. Application of the lognormal distribution. Brownian motion. (10%).


AIMS OF MODULE 1. To introduce the concepts and terminology of financial mathematics. 2. To introduce modelling in finance. 3. To develop the properties of interest rates. To provide the student with the key tools of compound interest functions for modelling a range of annuity schemes. 4. To develop models for life insurance and endowment schemes. 5. To enable the students to analyse the behaviour of share prices. 6. To use a generalised cash-flow model to describe financial transactions. 7. To develop simple models of financial instruments such as bonds and shares.


LEARNING OUTCOMES On completion of the module, the student will be able to: 1. Construct, analyse and evaluate models for simple and compound interest problems. 2. Construct, solve and analyse equations of value for implied rates of interest. 3. Formulate and assess a variety of insurance and endowment schemes. 4. Create and evaluate potential models for the price of shares. 5. Create and critically assess discounted cash-flow models for project appraisal. 6. Construct, evaluate and analyse models for investments and securities. 7. Design, build, investigate and evaluate forward contract using arbitrage-free pricing methods.


PREREQUISITES None


COREQUISITE(S) None


DISTANCE LEARNING DELIVERY None


LEARNING, TEACHING AND ASSESSMENT STRATEGY Material will be delivered by lectures supported by seminars and directed learning. Examination assesses Learning Outcomes 1- 7. Assignment assesses Learning Outcomes 1, 3 and 4.


IMPLICATIONS FOR CHOICE None


NOTIONAL STUDENT WORKLOAD Lectures 39 Seminars 13 Directed Learning 39 Independent Learning 69 Formal Assessment 40 Total 200 hours.

Other Modules within Mathematics BSc (Hons)

Year 1

MS0262 - Calculus (CORE, 20 Credits)

MS0401 - Modelling (CORE, 20 Credits)

MS0402 - Computational Mathematics (CORE, 20 Credits)

MS0409 - Dynamics (CORE, 20 Credits)

MS0410 - Statistics (CORE, 20 Credits)

MS0411 - Algebra and Analysis (CORE, 20 Credits)

Year 2

CG0026 - Further Computational Mathematics (CORE, 20 Credits)

CG0027 - Vector Calculus and Fluid Dynamics (CORE, 20 Credits)

CG0029 - Applied Statistical Methods (CORE, 20 Credits)

CG0500 - Further Differential Equations (CORE, 20 Credits)

MS0503 - Applied Modelling (CORE, 20 Credits)

MS0504 - Dynamics and Operational Research (CORE, 20 Credits)

Year 3

CM0567 - CEIS Professional Placement (CORE, 0 Credits)

Year 4

CG0010 - Financial Mathematics (OPTION, 20 Credits)

CG0012 - Reliability and Medical Statistics (OPTION, 20 Credits)

CG0013 - Algebraic Codes and Mathematical Cryptology (OPTION, 20 Credits)

CG0035 - Project (OPTION, 20 Credits)

CG0139 - Advanced Mathematical Modelling (CORE, 20 Credits)

MS0269 - Fluid Dynamics and Elasticity (OPTION, 20 Credits)

MS0602 - Dynamical Systems (OPTION, 20 Credits)

MS0603 - Advanced Statistical Methods (OPTION, 20 Credits)

MS0604 - Further O.R. and Time Series (OPTION, 20 Credits)

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