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# Certificate in Financial Maths & Modelling Syllabus

Certificate in Financial Maths & Modelling Syllabus Overview The Certificate in Financial Maths & Modelling provides a rigorous and integrated set of quantitative tools to understand and ex plain financial instruments, financial risk and corporate value and the fundamentally important relationship between them.The emphasis throughout is on t he practical modelling of real life problems and opportunities.

Techniques such as no-arbitrage pricing, duration, convexity and portfolio analysis – including the trade-off between risk and return – are explained and applied.The course analyses the use of options for financial risk management, and the valuation of different types of option using binomial pricing models, the Black Scholes model and other techniques.

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It also int roduces and applies Value at Risk measures, their potential us es and their limitations.

Study Unit 1 – Fundamental concepts in financial maths and modelling Study Unit 1 introduces the fundamental concepts of financial maths and modelling in the five areas of: interest rat e mathematics; modelling the values of a series of fixed or growing future cashflows; modelling the term structure of int erest rates using no arbitrage relationships; selected issues in probability and statistical models; and modelling the maths of Value at Risk.

Study Unit 2 – Modelling the maths of debt Study Unit 2 looks at modelling the maths of debt in the main areas of: present values, fut ure cash flows, timing and risk; and interest rat e sensitivity and duration models, in particular value relationships with respect to yield, maturity, coupon rate and coupon frequency.

Study Unit 3 – Modelling the maths of foreign exchange Study Unit 3 introduces the c oncepts of modelling t he maths of foreign exchange in the four areas of: quoting conventions; hedging using forward foreign exchange cont racts; the relationships bet ween foreign exchange rates, interest rates and inflation rates and applying VaR to foreign exchange risk management. Study Unit 4 – Modelling the maths of derivatives Study Unit 4 covers the maths and modelling of derivatives in t he two areas of: int roduction to derivatives mathematics; and modelling capital market swap mathematics.

Study Unit 5 – Modelling the maths of options Study Unit 5 covers the maths and modelling of options in the four areas of: option payoff mathematics; option payoff maths in the context of hedging; option valuation modelling; and options arbitrage and the put-call parity relationship. Study Unit 6 – Modelling the maths of portfolios and corporate finance Study Unit 6 introduces the fundamental concepts of modelling the maths of port folios and corporate finance in the t wo areas of: modelling port folios – analysis of risk and return, and modelling for corporate finance – corporate valuation and the impact of changing capit al structure. Association of Corporate Treasurers (01. 04. 11, subject to change) Study Unit 1 – Fundamental concepts in financial maths and modelling Unit introduction 1. 0. 1 Notation and rules of algebra 1. 0. 2 Financial modelling Section 1 – Interest rate mathematics 1. 1. 1 Interest calculations and quoting conventions 1. 1. 2 The time-value relationship Section 2 – Modelling values of a series of future cashflows 1. 2. 1 Infinite series cashflows (perpetuities) and their valuation 1. 2. Finite series cashflows (annuities) and their valuation Section 3 – Modelling the term structure of interest rate s: no arbitrage relationships 1. 3. 1 Zero coupon, forward and par structures of interest rates: different forms of yield curves 1. 3. 2 No arbitrage relationships between zero coupon, forward and par rates Section 4 – Probability and stati sti cal models: selected issue s 1. 4. 1 Measures of central location (or central tendency), dispersion and correlation 1. 4. 2 Frequency distributions in theory and in practice Section 5 – Modelling the maths of Value at Risk 1. . 1 Modelling the maths of Value at Risk for single risks 1. 5. 2 Extending the modelling of Value at Risk Study Unit 2 – Modelling the maths of debt Section 1 – Short term debt 2. 1. 1 Short term debt issuers, market participants and market conventions 2. 1. 2 Calculation of interest and valuation of short term debt instruments Section 2 – Longer term debt 2. 2. 1 Analysis and valuation of bonds 2. 2. 2 Real interest rates and inflation indexing Section 3 – Interest rate sensitivity and duration models 2. 3. Duration and int erest rat e price sensitivity, relative and absolute measures 2. 3. 2 Interest rate immunisation, convexity and modified convexity Study Unit 3 – Modelling the maths of foreign exchange Section 1 – Foreign exchange mathematics 3. 1. 1 Converting between currencies: using spot foreign exchange rates 3. 1. 2 Converting between currencies: determining and using forward foreign exchange rat es 3. 1. 3 The maths of foreign exchange risk management 3. 1. 4 Applying Value at Risk to foreign exchange risk management

Study Unit 4 – Modelling the maths of derivatives Section 1 – Introduction to derivative s mathematics 4. 1. 1 Payoffs for fixing derivatives and options 4. 1. 2 The maths of FRAs: cashflows, hedging, valuation and basis risk 4. 1. 3 Futures contracts: cashflows, hedging and valuation Section 2 – Modelling swap mathematics 4. 2. 1 The maths of capital market swaps including interest rate swaps 4. 2. 2 The maths of cross-currency interest rate swaps © Association of Corporate Treasurers (01. 04. 11, subject to change) Study Unit 5 – Modelling the maths of options

Section 1 – Option payoff mathematics 5. 1. 1 Payoffs from trading strategies with single options 5. 1. 2 Payoffs from trading strategies involving more than one option Section 2 – Option payoff maths: hedging and hedged results achieved 5. 2. 1 Hedging a portfolio: options plus underlying asset/(liability) 5. 2. 2 Hedging corporate exposures with options Section 3 – Option valuation modelling 5. 3. 1 Binomial option valuation models 5. 3. 2 Black Scholes option pricing model 5. 3. 3 Arbitrage and the put-call parity relationship

Study Unit 6 – Modelling the maths of portfolios and corporate finance Section 1 – Modelling portfolios: analysi s of ri sk and return 6. 1. 1 Modelling simple port folios: analysis of risk and return 6. 1. 2 Modelling multi-asset port folios & portfolios including liabilities Section 2 – Modelling for corporate finance 6. 2. 1 Modelling the cost of corporate capital 6. 2. 2 Modelling the relationship between corporate value and capital structure 6. 2. 3 Modelling corporate valuation © Association of Corporate Treasurers (01. 04. 11, subject to change)

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