Mathematics of the Financial Markets : Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

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Mathematics of Financial Markets; Contents; Foreword; Main Notations; Introduction; Part I The Deterministic Environment; 1 Prior to the yield curve: spot and forward rates; 1.1 INTEREST RATES, PRESENT AND FUTURE VALUES, INTEREST COMPOUNDING; 1.1.1 Counting the number of days; 1.2 DISCOUNT FACTORS; 1.3 CONTINUOUS COMPOUNDING AND CONTINUOUS RATES; 1.4 FORWARD RATES; 1.4.1 Generalization: forwards and discount factors; 1.5 THE NO ARBITRAGE CONDITION; FURTHER READING; 2 The term structure or yield curve; 2.1 INTRODUCTION TO THE YIELD CURVE; 2.2 THE YIELD CURVE COMPONENTS

2.2.1 The money market side2.2.2 Capital market side: the case of the risk-free yield curve; 2.2.3 Capital market side: the case of the swap yield curve; 2.3 BUILDING A YIELD CURVE: METHODOLOGY; 2.4 AN EXAMPLE OF YIELD CURVE POINTS DETERMINATION; 2.5 INTERPOLATIONS ON A YIELD CURVE; FURTHER READING; 3 Spot instruments; 3.1 SHORT-TERM RATES; 3.2 BONDS; 3.2.1 Bond pricing; 3.2.2 Duration; 3.2.3 Convexity; 3.3 CURRENCIES; 3.3.1 Introduction to the currencies spot market; 3.3.2 Spot quotations; FURTHER READING; 4 Equities and stock indexes; 4.1 STOCKS VALUATION

4.1.1 Discounted cash flows (DCF) method4.1.2 The Gordon-Shapiro method; 4.1.3 The case of stocks not distributing dividends; 4.1.4 The real option method; 4.1.5 The book value method; 4.2 STOCK INDEXES; 4.3 THE PORTFOLIO THEORY; 4.3.1 Introduction to the Portfolio Theory; 4.3.2 Risk and return measures; 4.3.3 The Markowitz model; 4.3.4 Sharpe's CAPM; 4.3.5 The APT model (Roll and Ross); 4.3.6 CAPM versus APT; 4.3.7 The four-moments CAPM; FURTHER READING; 5 Forward instruments; 5.1 THE FORWARD FOREIGN EXCHANGE; 5.1.1 Forward exchange operations; 5.1.2 Forex (or FX) swaps

5.1.3 Forward forex swaps or forward-forward transactions5.1.4 The NDF market; 5.2 FRAs; 5.2.1 Principle and calculation; 5.2.2 Example of application; 5.3 OTHER FORWARD CONTRACTS; 5.3.1 Forward contracts on equities; 5.3.2 Forward contracts on bonds; 5.4 CONTRACTS FOR DIFFERENCE (CFD); FURTHER READING; 6 Swaps; 6.1 DEFINITIONS AND FIRST EXAMPLES; 6.1.1 A first example of an IRS, on a debt (data from February 2002); 6.1.2 An example of CRS liability swap (data from February 2002); 6.1.3 Unwinding a swap; 6.2 PRIOR TO AN IRS SWAP PRICING METHOD; 6.3 PRICING OF AN IRS SWAP

6.4 (RE)VALUATION OF AN IRS SWAP6.5 THE SWAP (RATES) MARKET; 6.6 PRICING OF A CRS SWAP; 6.7 PRICING OF SECOND-GENERATION SWAPS; 6.7.1 Zero-coupon swap; 6.7.2 EONIA and other basis swap; 6.7.3 In-arrear swap; 6.7.4 Constant maturity swap; 6.7.5 Quanto or diff swap; 6.7.6 Swapping other types of cash flows: performance swaps; FURTHER READING; 7 Futures; 7.1 INTRODUCTION TO FUTURES; 7.1.1 Margining system; 7.1.2 Settlement of the future contract at maturity; 7.2 FUTURES PRICING; 7.2.1 Theoretical price of a future; 7.2.2 Theoretical versus market future price; 7.2.3 The implied repo rate (IRR)

7.2.4 Future versus forward prices

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