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【金融数学教程】A course in financial calculus-[pdf]-[Alison Etheridge]

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    发表于 2017-10-25 10:50:25 | 显示全部楼层 |阅读模式
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    书籍信息:
    标题: A course in financial calculus【金融数学教程】
    语言: English
    格式: pdf
    大小: 1.3M
    页数: 206
    年份: 2002
    作者: Alison Etheridge
    出版社: CUP


    简介

    This text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus. The Black-Scholes pricing formula is first derived in the simplest financial context. Subsequent chapters are devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A large number of exercises and examples illustrate how the methods and concepts can be applied to realistic financial questions.


    目录
    Cover......Page 1
    Half-title......Page 3
    Title......Page 5
    Copyright......Page 6
    Contents......Page 7
    Preface......Page 9
    Derivatives......Page 11
    The pricing problem......Page 12
    Packages......Page 13
    The risk-free rate......Page 14
    Arbitrage pricing......Page 15
    Pricing a European call......Page 16
    1.4 A ternary model......Page 18
    1.5 A characterisation of no arbitrage......Page 19
    A market with N assets......Page 20
    Arbitrage pricing......Page 21
    1.6 The risk-neutral probability measure......Page 23
    Expectation recovered......Page 24
    Risk-neutral pricing......Page 25
    Complete markets......Page 26
    Trading in two different markets......Page 27
    Exercises......Page 28
    2.1 The multiperiod binary model......Page 31
    The cash bond......Page 32
    Binomial trees......Page 33
    2.2 American options......Page 36
    Put on nondividendpaying stock......Page 37
    2.3 Discrete parameter martingales and Markov processes......Page 38
    Stochastic processes......Page 39
    Conditional expectation......Page 40
    The martingale property......Page 42
    Examples......Page 44
    New martingales from old......Page 45
    Discrete stochastic integrals......Page 46
    The Fundamental Theorem of Asset Pricing......Page 47
    Optional stopping......Page 48
    Compensation......Page 51
    American options and supermartingales......Page 52
    2.5 The Binomial Representation Theorem......Page 53
    From martingale representation to replicating portfolio......Page 54
    2.6 Overture to continuous models......Page 55
    Under the martingale measure......Page 56
    Exercises......Page 57
    A characterisation of simple random walks......Page 61
    Definition of Brownian motion......Page 63
    Behaviour of Brownian motion......Page 65
    A polygonal approximation......Page 66
    Convergence to Brownian motion......Page 67
    Stopping times......Page 69
    The reflection principle......Page 70
    Hitting a sloping line......Page 71
    3.4 Martingales in continuous time......Page 73
    Martingales......Page 74
    Brownian hitting time distribution......Page 76
    Exercises......Page 77
    Summary......Page 81
    4.1 Stock prices are not differentiable......Page 82
    Bounded variation and arbitrage......Page 83
    A differential equation for the stock price......Page 84
    Quadratic variation......Page 85
    Integrating Brownian motion against itself......Page 86
    Defining the integral......Page 87
    Integrating simple functions......Page 88
    Construction of the Ito integral......Page 91
    Other integrators......Page 93
    The stochastic chain rule......Page 95
    Geometric Brownian motion......Page 97
    Ito’s formula for geometric Brownian motion......Page 98
    Levy’s characterisation of Brownian motion......Page 100
    Stochastic differential equations......Page 101
    Solving stochastic differential equations......Page 102
    Covariation......Page 103
    4.5 The Girsanov Theorem......Page 106
    Change of measure in the continuous world......Page 107
    4.6 The Brownian Martingale Representation Theorem......Page 110
    4.8 The Feynman–Kac representation......Page 112
    Solving pde’s probabilistically......Page 113
    Kolmogorov equations......Page 114
    Exercises......Page 117
    5.1 The basic Black–Scholes model......Page 122
    Self- financing strategies......Page 123
    An equivalent martingale measure......Page 125
    The Fundamental Theorem of Asset Pricing......Page 126
    5.2 Black–Scholes price and hedge for European options......Page 128
    Pricing calls and puts......Page 129
    Hedging calls and puts......Page 130
    5.3 Foreign exchange......Page 132
    Change of numeraire......Page 135
    Continuous payments......Page 136
    Periodic dividends......Page 139
    5.5 Bonds......Page 141
    5.6 Market price of risk......Page 142
    Martingales and tradables......Page 143
    Exercises......Page 144
    6.1 European options with discontinuous payoffs......Page 149
    Digitals and pin risk......Page 150
    6.2 Multistage options......Page 151
    General strategy......Page 152
    Compound options......Page 153
    6.3 Lookbacks and barriers......Page 154
    Joint distribution of the stock price and its minimum......Page 155
    An expression for the price......Page 157
    6.4 Asian options......Page 159
    6.5 American options......Page 160
    Continuous time......Page 161
    An explicit solution......Page 163
    Exercises......Page 164
    Summary......Page 169
    The model......Page 170
    Second step to replication......Page 171
    The generalised Black–Scholes equation......Page 172
    Correlated security prices......Page 173
    Multifactor Ito formula......Page 174
    Change of measure......Page 176
    A martingale measure......Page 177
    Replicating the claim......Page 178
    The multidimensional Black–Scholes equation......Page 180
    Numeraires......Page 181
    Quantos......Page 182
    Pricing a quanto forward contract......Page 183
    A Poisson process of jumps......Page 185
    Poisson exponential martingales......Page 187
    Change of measure......Page 188
    Market price of risk......Page 189
    Multiple noises......Page 190
    Hedging error......Page 191
    Stochastic volatility and implied volatility......Page 193
    Exercises......Page 195
    Further topics in financial mathematics:......Page 199
    Additional references from the text:......Page 200
    Martingales and other stochastic processes......Page 201
    Miscellaneous......Page 202
    Index......Page 203

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