The aim of the Financial Mathematics module is to provide a grounding in financial mathematics and its simple applications. This module covers all required material for the Institute and Faculty of Actuaries CT1 syllabus (Financial Mathematics, Core Technical).
Syllabus
1. The time value of money
1.1 Simple interest
1.2 Compound interest
1.3 Nominal and effective interest rates
1.4 The force of interest
1.5 Real and money interest rates
1.6 Discounting and accumulating
2. Cash flows and investment project appraisal
2.1 Cash flows and their value
2.2 Net present value and discounted cash flow
2.3 Equations of value
2.4 The internal rate of return
2.5 The comparison of two investment projects
2.6 Measurement of investment project performance
3. Annuities and loan schedules
3.1 Annuities
3.2 Perpetuities
3.3 Deferred Annuities
3.4 Varying annuities
3.5 Loan schedules
4. The valuation of securities
4.1 Fixed-interest securities
4.2 Related assets
4.3 Prices and yield
4.4 The effect of the term to redemption on the yield
4.5 Optional redemption dates
4.6 Real returns and index-linked securities
5. Capital Gains Tax
5.1 Fixed-interest securities and running yields
5.2 Income tax and capital gains tax
5.3 Offsetting capital losses against capital gains
5.4 Indexation of Capital Gains Tax
5.5 Inflation adjustments
6. Term structures and immunization
6.1 Spot and forward rates
6.2 Duration
6.3 Convexity
6.4 Redington immunisation
7. Arbitrage and forward contracts
7.1 Arbitrage
7.2 Forwards contract
7.3 Calculating the forward price
7.4 Speculation, hedging, gearing (leverage)
7.5 The value of a forward contract prior to maturity
8. Stochastic interest rate models
8.1 Simple model
8.2 Independent annual rates of return
8.3 The log-normal distribution
On completion of this module, students should be able to:
- Describe how to take into account the time value of money using the concepts of compound interest and discounting.
- Show how interest rates or discount rates may be expressed in terms of different time periods.
- Demonstrate a knowledge and understanding of real and money interest rates.
- Calculate the present value and the accumulated value of a stream of payments using specified rates of interest, and the net present value at a real rate of interest.
- Apply a generalised cash flow model to analyse financial transactions.
- Derive and solve equations of value.
- Show how discounted cash flow techniques can be used in measurement of investment project performance.
- Derive formulae for different types of annuities.
- Describe how a loan may be repaid by regular instalments of interest and capital.
- Describe the investment and risk characteristics of typical assets available for investment purposes.
- Analyse elementary compound interest problems allowing for both income tax and capital gains tax liabilities and calculate the real yield from the fixed-interest securities.
- Show an understanding of the term structure of interest rates; evaluate the duration and convexity of a cash flow sequence, and their use in Redington immunisation of a portfolio of liabilities.
- Define the concept of arbitrage, explain the significance of the no-arbitrage assumption and use this assumption to calculate the forward price of a number of derivative-type contracts.
- Show an understanding of simple stochastic models for investment returns.
Syllabus
1. The time value of money
1.1 Simple interest
1.2 Compound interest
1.3 Nominal and effective interest rates
1.4 The force of interest
1.5 Real and money interest rates
1.6 Discounting and accumulating
2. Cash flows and investment project appraisal
2.1 Cash flows and their value
2.2 Net present value and discounted cash flow
2.3 Equations of value
2.4 The internal rate of return
2.5 The comparison of two investment projects
2.6 Measurement of investment project performance
3. Annuities and loan schedules
3.1 Annuities
3.2 Perpetuities
3.3 Deferred Annuities
3.4 Varying annuities
3.5 Loan schedules
4. The valuation of securities
4.1 Fixed-interest securities
4.2 Related assets
4.3 Prices and yield
4.4 The effect of the term to redemption on the yield
4.5 Optional redemption dates
4.6 Real returns and index-linked securities
5. Capital Gains Tax
5.1 Fixed-interest securities and running yields
5.2 Income tax and capital gains tax
5.3 Offsetting capital losses against capital gains
5.4 Indexation of Capital Gains Tax
5.5 Inflation adjustments
6. Term structures and immunization
6.1 Spot and forward rates
6.2 Duration
6.3 Convexity
6.4 Redington immunisation
7. Arbitrage and forward contracts
7.1 Arbitrage
7.2 Forwards contract
7.3 Calculating the forward price
7.4 Speculation, hedging, gearing (leverage)
7.5 The value of a forward contract prior to maturity
8. Stochastic interest rate models
8.1 Simple model
8.2 Independent annual rates of return
8.3 The log-normal distribution
On completion of this module, students should be able to:
- Describe how to take into account the time value of money using the concepts of compound interest and discounting.
- Show how interest rates or discount rates may be expressed in terms of different time periods.
- Demonstrate a knowledge and understanding of real and money interest rates.
- Calculate the present value and the accumulated value of a stream of payments using specified rates of interest, and the net present value at a real rate of interest.
- Apply a generalised cash flow model to analyse financial transactions.
- Derive and solve equations of value.
- Show how discounted cash flow techniques can be used in measurement of investment project performance.
- Derive formulae for different types of annuities.
- Describe how a loan may be repaid by regular instalments of interest and capital.
- Describe the investment and risk characteristics of typical assets available for investment purposes.
- Analyse elementary compound interest problems allowing for both income tax and capital gains tax liabilities and calculate the real yield from the fixed-interest securities.
- Show an understanding of the term structure of interest rates; evaluate the duration and convexity of a cash flow sequence, and their use in Redington immunisation of a portfolio of liabilities.
- Define the concept of arbitrage, explain the significance of the no-arbitrage assumption and use this assumption to calculate the forward price of a number of derivative-type contracts.
- Show an understanding of simple stochastic models for investment returns.
- Module Supervisor: Junlei Hu