The Mathematics of Financial Modelingand Investment Management

(Brent) #1

Frontmatter Page iv Monday, March 8, 2004 10:06 AM


iv Contents

Trading Locations 45

Stock Market Indicators 46

Trading Arrangements 48

Bonds 51

Maturity 51

Par Value 52

Coupon Rate 52

Provisions for Paying off Bonds 55

Options Granted to Bondholders 56

Futures and Forward Contracts 57

Futures versus Forward Contracts 58

Risk and Return Characteristics of Futures Contracts 59

Pricing of Futures Contracts 59

The Role of Futures in Financial Markets 63

Options 64

Risk-Return for Options 66

The Option Price 66

Swaps 69

Caps and Floors 70

Summary 71

CHAPTER 3
Milestones in Financial Modeling and Investment Management 75

The Precursors: Pareto, Walras, and the Lausanne School 76

Price Diffusion: Bachelier 78

The Ruin Problem in Insurance: Lundberg 80

The Principles of Investment: Markowitz 81

Understanding Value: Modigliani and Miller 83

Modigliani-Miller Irrelevance Theorems and the
Absence of Arbitrage 84

Efficient Markets: Fama and Samuelson 85

Capital Asset Pricing Model: Sharpe, Lintner, and Mossin 86

The Multifactor CAPM: Merton 87

Arbitrage Pricing Theory: Ross 88

Arbitrage, Hedging, and Option Theory:
Black, Scholes, and Merton 89

Summary 90

CHAPTER 4
Principles of Calculus 91

Sets and Set Operations 93

Proper Subsets 93

Empty Sets 95

Union of Sets 95

Intersection of Sets 95

Elementary Properties of Sets 96

Distances and Quantities 96

n-tuples 97

Distance 98
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