Financial Mathematics

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Use a generalised cash-flow model to describe financial transactions.
• Analyse straightforward compound interest problems, and solve resulting equations of value, including for the implied rate of return.
• Calculate the discounted mean term or volatility of an asset or liability and analyse whether an asset-liability position is matched or immunized.
• Demonstrate an understanding of behavioural economics.
• Calculate the forward price and value of a forward contract using no-arbitrage pricing.
• Apply discounted cash flow techniques to the valuation of securities, including the effects of taxation.
• Demonstrate an understanding of the term structure of interest rates.
• Take into account the time value of money by using the concepts of compound interest and discounting.
• Describe how a loan may be repaid by regular instalments of interest and capital.
• Demonstrate an understanding of the nature and use of simple stochastic interest rate models.
• Define and use standard compound interest functions.
• Calculate the present value and accumulated value of a cash flow of equal or unequal payments, at a specified rate of interest, and at a real rate of interest, assuming a given rate of inflation.
• Apply discounted cash flow techniques to investment project appraisal.
• Describe the main investment and risk characteristics of the standard asset classes available for investment purposes.
• Demonstrate how interest rates and discount rates change when the underlying time period is altered.

• Simple and compound interest. Time value of money. Rate of interest, rate of discount, and force of interest. Accumulated values and discounted values. Accumulation and discounting of a (possibly infinite) cash flow to a given time, where both the rate of cash flow and the force of interest may be time-varying.
• Relationships between rates of interest and discount over different time periods. Nominal rates, effective rates, rates payable multiple times per annum.
• Definition of the standard compound interest functions and relationships between them.
• Generalised cash flow modelling. Equation of value for a cash flow problem, and methods of solution.
• Loans. Equation of value corresponding to periodic repayment of a loan. Interest and capital content of annuity payments where the annuity is used to repay a loan. Consumer credit transactions. Annual Percentage Rate of Charge (APR).
• Net present value (NPV), accumulated profit, and internal rate of return (IRR) for investment projects.
• Investment project appraisal using NPV and IRR. Real rate of return in presence of inflation.
• Behavioural economics. Expected utility theory, prospect theory, framing, heuristics, and biases. The Bernartzi and Thaler solution to the equity premium puzzle.
• Ordinary shares. Constant dividend growth model of share valuation. Fixed-interest securities. Present value and redemption yield for a fixed-interest security, including effects of taxation.
• Yield curves and the term structure of interest rates.
• Investment and risk characteristics of standard asset classes (Government fixed-interest securities, other fixed-interest securities, equities, etc.) available for investment purposes.
• Discounted mean term, volatility, convexity. Matching of assets and liabilities, immunization.
• Simple stochastic interest rate models. Mean, variance, and distribution function for the accumulated amount of an initial investment, and applications.
• Spot and forward interest rates. Forward contracts. The concept of no-arbitrage pricing and its use in determining the fair value of a forward contract.

Teaching and learning methods

Lectures, problem classes, workshops, assigned problems and solutions, class test and solutions, assignment and solutions, office hours, and private study.

Resources & Reading list

General Resources

Garrett is an essential text and covers all of the syllabus. Students should obtain a copy. Problems will be assigned from this text..

McCutcheon and Scott covers most of the syllabus, is a good second choice, and, like Garrett, has a large number of good problems..

Hull covers the part of the syllabus relating to derivative securities, though this is also covered by Garrett..

Kellison, Butcher and Nesbitt, and Broverman all cover similar ground..

Textbooks

GARRETT, S.J. (2013). An Introduction to the Mathematics of Finance: A Deterministic Approach. Butterworth-Heinemann.

KELLISON, S.G (2008). Theory of Interest. Irwin.

HULL, J.C., (2014). Options, Futures, and Other Derivatives. Prentice Hall.

BROVERMAN, S.A. (2010). Mathematics of Investment and Credit. Actex Publications.

McCUTCHEON, J.J. and SCOTT, W.F., (1986). An Introduction to the Mathematics of Finance. Heinemann.

BUTCHER, M.V. and NESBITT, C.J. (1971). Mathematics of Compound Interest. Ulrich’s Books.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat Information

Repeat type: Internal & External