# KC6001 - Financial Mathematics

## What will I learn on this module?

The module introduces the concepts and terminology of financial mathematics and modelling in finance. You will learn about
the properties of interest rates and the key tools of compound interest functions for modelling a range of annuity schemes. The module develops models for life insurance and endowment schemes and enables the students to analyse the behaviour of share prices. The generalised cash-flow model is introduced to describe financial transactions. The student learns how to develop simple models of financial instruments such as bonds and shares.

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.
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.
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.
Investments: Types of investments. Valuation of fixed interest securities and uncertain income securities. Real rates of interest. Effects of inflation. Capital gains tax.
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.
Life Insurance: Term insurance and whole life insurance. Curtate future lifetime. Life tables, expectation of life. Annual and monthly premium. Endowments. Payment at death.
Stochastic Interest Rates: Varying interest rates. Independent rates of return. Expected values. Application of the lognormal distribution. Brownian motion.

### How will I learn on this module?

You will learn through a combination of lectures and skills periods focussing on problem solving where you will be able to obtain help. Lectures allow students to experience and understand the formalism of the required mathematical techniques as well as include relevant examples and guided in-class exercise-solving sessions between more theoretical expositions. Students have an opportunity to enhance their understanding of the subject through exercises which promote both independent learning and problem solving within peer groups. The exercise classes will also be an opportunity to present you with open research problems, and will strengthen your transferable skills and employability. Northumbria’s computer labs and facilities are fully equipped with the latest industry-standard software such as Matlab, Excel and others, which will be used to support independent study and learning. Further technology-enhanced resources such as e-lecture notes, seminar sheets with answers and solution and past-paper questions will be provided via the e-learning portal.

### How will I be supported academically on this module?

In addition to academic contact with the module team during lectures and exercise classes, students are encouraged to develop their curiosity by making direct contact with the module team either via email or the open-door policy operated throughout the programme. Students will also be regularly referred to supporting resources including relevant texts and relevant multimedia materials. References to these resources will be made available through the e-learning portal and in lectures and seminars.

### What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

### What will I be expected to achieve?

Knowledge & Understanding:
1. Apply equation of value in the context of the discounted cash flow model (KU1);
2. Compose appropriate models for valuating securities (KU2, KU3);
3. Understand and apply the theory of interest rates (KU3).

Intellectual / Professional skills & abilities:
4. Perform project appraisal and evaluate the performance of the project/company on a stock market (IPSA1, IPSA2, IPSA3).

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. Increases proficiency and independence in exploiting rigorous mathematical techniques to study economical and financial problems (PVA1, PVA3, PVA4).

### How will I be assessed?

SUMMATIVE
1. Coursework (30%) – 1, 3, 4, 5
2. Examination (70%) – 1, 2, 3, 5

FORMATIVE
Exercise Classes – 1, 2, 3, 4, 5

Students will be assessed by two formal assessments with weights 30% (coursework) and 70% (exam) respectively. The examinations will cover all topics from the module.

Formative feedback will be provided on seminar work which will include problems designed to aid student understanding.

None

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### Module abstract

The module will introduce you to the concepts and terminology of financial mathematics and modelling in finance. You will learn properties of interest rates and the key tools of compound interest functions for modelling a range of annuity schemes. The module develops models for life insurance and endowment schemes and enables the students to analyse the behaviour of share prices. The generalised cash-flow model is introduced to describe financial transactions. You will learn how to develop simple models of financial instruments such as bonds and shares, enhancing skills that are essential to your future careers and/or postgraduate study. You will be assessed by course work in the form of individual assignment (30%) and by a written, closed-book examinations (70%). The examination will cover all topics from the module.

### Course info

UCAS Code G100

Credits 20

Mode of Study 3 years full-time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2024

## Mathematics BSc (Hons)

All information is accurate at the time of sharing.

Full time Courses starting in 2023 are primarily delivered via on-campus face to face learning but may include elements of online learning. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to flex accordingly to ensure the health and safety of our students and staff.

Contact time is subject to increase or decrease in line with additional restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors, potentially to a full online offer, should further restrictions be deemed necessary in future. Our online activity will be delivered through Blackboard Ultra, enabling collaboration, connection and engagement with materials and people.

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