(1元)Tomas Bjork 2009-Arbitrage Theory in Continuous Time,Third Edition

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CONTENTS
1 Introduction 1
1.1 Problem Formulation 1
2 The Binomial Model 5
2.1 The One Period Model 5
2.1.1 Model Description 5
2.1.2 Portfolios and Arbitrage 6
2.1.3 Contingent Claims 9
2.1.4 Risk Neutral Valuation 11
2.2 The Multiperiod Model 15
2.2.1 Portfolios and Arbitrage 15
2.2.2 Contingent Claims 17
2.3 Exercises 25
2.4 Notes 25
3 A More General One Period Model 26
3.1 The Model 26
3.2 Absence of Arbitrage 27
3.3 Martingale Measures 32
3.4 Martingale Pricing 34
3.5 Completeness 35
3.6 Stochastic Discount Factors 38
3.7 Exercises 39
4 Stochastic Integrals 40
4.1 Introduction 40
4.2 Information 42
4.3 Stochastic Integrals 44
4.4 Martingales 46
4.5 Stochastic Calculus and the Itˆo Formula 49
4.6 Examples 54
4.7 The Multidimensional Itˆo Formula 57
4.8 Correlated Wiener Processes 59
4.9 Exercises 63
4.10 Notes 65
5 Differential Equations 66
5.1 Stochastic Differential Equations 66
5.2 Geometric Brownian Motion 67
5.3 The Linear SDE 70
5.4 The Infinitesimal Operator 71
5.5 Partial Differential Equations 72
5.6 The Kolmogorov Equations 76
5.7 Exercises 79
5.8 Notes 83
6 Portfolio Dynamics 84
6.1 Introduction 84
6.2 Self-financing Portfolios 87
6.3 Dividends 89
6.4 Exercises 91
7 Arbitrage Pricing 92
7.1 Introduction 92
7.2 Contingent Claims and Arbitrage 93
7.3 The Black–Scholes Equation 98
7.4 Risk Neutral Valuation 102
7.5 The Black–Scholes Formula 104
7.6 Options on Futures 106
7.6.1 Forward Contracts 106
7.6.2 Futures Contracts and the Black Formula 107
7.7 Volatility 108
7.7.1 Historic Volatility 109
7.7.2 Implied Volatility 110
7.8 American Options 110
7.9 Exercises 112
7.10 Notes 114
8 Completeness and Hedging 115
8.1 Introduction 115
8.2 Completeness in the Black–Scholes Model 116
8.3 Completeness—Absence of Arbitrage 121
8.4 Exercises 122
8.5 Notes 124
9 Parity Relations and Delta Hedging 125
9.1 Parity Relations 125
9.2 The Greeks 127
9.3 Delta and Gamma Hedging 130
9.4 Exercises 134
10 The Martingale Approach to Arbitrage Theory* 137
10.1 The Case with Zero Interest Rate 137
10.2 Absence of Arbitrage 140
10.2.1 A Rough Sketch of the Proof 141
10.2.2 Precise Results 144
10.3 The General Case 146
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关键词：Continuous Arbitrage Edition editio dition General 朋友

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