Copula Methods in Finance. John Wiley[2004.ISBN0470863447]

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Copula Methods in Finance. John Wiley[2004.ISBN0470863447]
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【书名】 Copula Methods in Finance
【作者】  Umberto Cherubini Elisa Luciano and Walter Vecchiato
【出版社】John Wiley
【版本】
【出版日期】2004
【文件格式】PDF【文件大小】5.5M
【页数】308页
【ISBN出版号】ISBN0470863447
【资料类别】统计学
【市面定价】$150($119 on Amazon)
【是否缺页】不缺页
【关键词】Copula , Finance
【内容简介】Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications.  It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis.  Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues.  Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactionsCopula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications.  It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis.  Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues.  Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions
【目录】

       Contents
Preface xi
List of Common Symbols and Notations xv
1 Derivatives Pricing, Hedging and Risk Management: The State of the Art 1
1.1 Introduction 1
1.2 Derivative pricing basics: the binomial model 2
1.2.1 Replicating portfolios 3
1.2.2 No-arbitrage and the risk-neutral probability measure 3
1.2.3 No-arbitrage and the objective probability measure 4
1.2.4 Discounting under different probability measures 5
1.2.5 Multiple states of the world 6
1.3 The Black–Scholes model 7
1.3.1 Ito’s lemma 8
1.3.2 Girsanov theorem 9
1.3.3 The martingale property 11
1.3.4 Digital options 12
1.4 Interest rate derivatives 13
1.4.1 Affine factor models 13
1.4.2 Forward martingale measure 15
1.4.3 LIBOR market model 16
1.5 Smile and term structure effects of volatility 18
1.5.1 Stochastic volatility models 18
1.5.2 Local volatility models 19
1.5.3 Implied probability 20
1.6 Incomplete markets 21
1.6.1 Back to utility theory 22
1.6.2 Super-hedging strategies 23
1.7 Credit risk 27
1.7.1 Structural models 28
1.7.2 Reduced form models 31
1.7.3 Implied default probabilities 33
vi Contents
1.7.4 Counterparty risk 36
1.8 Copula methods in finance: a primer 37
1.8.1 Joint probabilities, marginal probabilities and copula functions 38
1.8.2 Copula functions duality 39
1.8.3 Examples of copula functions 39
1.8.4 Copula functions and market comovements 41
1.8.5 Tail dependence 42
1.8.6 Equity-linked products 43
1.8.7 Credit-linked products 44
2 Bivariate Copula Functions 49
2.1 Definition and properties 49
2.2 Fr´echet bounds and concordance order 52
2.3 Sklar’s theorem and the probabilistic interpretation of copulas 56
2.3.1 Sklar’s theorem 56
2.3.2 The subcopula in Sklar’s theorem 59
2.3.3 Modeling consequences 60
2.3.4 Sklar’s theorem in financial applications: toward a
non-Black–Scholes world 61
2.4 Copulas as dependence functions: basic facts 70
2.4.1 Independence 70
2.4.2 Comonotonicity 70
2.4.3 Monotone transforms and copula invariance 72
2.4.4 An application: VaR trade-off 73
2.5 Survival copula and joint survival function 75
2.5.1 An application: default probability with exogenous shocks 78
2.6 Density and canonical representation 81
2.7 Bounds for the distribution functions of sum of r.v.s 84
2.7.1 An application: VaR bounds 85
2.8 Appendix 87
3 Market Comovements and Copula Families 95
3.1 Measures of association 95
3.1.1 Concordance 95
3.1.2 Kendall’s τ 97
3.1.3 Spearman’s ρS 100
3.1.4 Linear correlation 103
3.1.5 Tail dependence 108
3.1.6 Positive quadrant dependency 110
3.2 Parametric families of bivariate copulas 112
3.2.1 The bivariate Gaussian copula 112
3.2.2 The bivariate Student’s t copula 116
3.2.3 The Fr´echet family 118
3.2.4 Archimedean copulas 120
3.2.5 The Marshall–Olkin copula 128
Contents vii
4 Multivariate Copulas 129
4.1 Definition and basic properties 129
4.2 Fr´echet bounds and concordance order: the multidimensional case 133
4.3 Sklar’s theorem and the basic probabilistic interpretation: the multidimensional
case 135
4.3.1 Modeling consequences 138
4.4 Survival copula and joint survival function 140
4.5 Density and canonical representation of a multidimensional copula 144
4.6 Bounds for distribution functions of sums of n random variables 145
4.7 Multivariate dependence 146
4.8 Parametric families of n-dimensional copulas 147
4.8.1 The multivariate Gaussian copula 147
4.8.2 The multivariate Student’s t copula 148
4.8.3 The multivariate dispersion copula 149
4.8.4 Archimedean copulas 149
5 Estimation and Calibration from Market Data 153
5.1 Statistical inference for copulas 153
5.2 Exact maximum likelihood method 154
5.2.1 Examples 155
5.3 IFM method 156
5.3.1 Application: estimation of the parametric copula for market data 158
5.4 CML method 160
5.4.1 Application: estimation of the correlation matrix for a Gaussian
copula 160
5.5 Non-parametric estimation 161
5.5.1 The empirical copula 161
5.5.2 Kernel copula 162
5.6 Calibration method by using sample dependence measures 172
5.7 Application 174
5.8 Evaluation criteria for copulas 176
5.9 Conditional copula 177
5.9.1 Application to an equity portfolio 178
6 Simulation of Market Scenarios 181
6.1 Monte Carlo application with copulas 181
6.2 Simulation methods for elliptical copulas 181
6.3 Conditional sampling 182
6.3.1 Clayton n-copula 184
6.3.2 Gumbel n-copula 185
6.3.3 Frank n-copula 186
6.4 Marshall and Olkin’s method 188
6.5 Examples of simulations 191
7 Credit Risk Applications 195
7.1 Credit derivatives 195
viii Contents
7.2 Overview of some credit derivatives products 196
7.2.1 Credit default swap 196
7.2.2 Basket default swap 198
7.2.3 Other credit derivatives products 199
7.2.4 Collateralized debt obligation (CDO) 199
7.3 Copula approach 202
7.3.1 Review of single survival time modeling and calibration 202
7.3.2 Multiple survival times: modeling 203
7.3.3 Multiple defaults: calibration 205
7.3.4 Loss distribution and the pricing of CDOs 206
7.3.5 Loss distribution and the pricing of homogeneous basket default
swaps 208
7.4 Application: pricing and risk monitoring a CDO 210
7.4.1 Dow Jones EuroStoxx50 CDO 210
7.4.2 Application: basket default swap 210
7.4.3 Empirical application for the EuroStoxx50 CDO 212
7.4.4 EuroStoxx50 pricing and risk monitoring 216
7.4.5 Pricing and risk monitoring of the basket default swaps 221
7.5 Technical appendix 225
7.5.1 Derivation of a multivariate Clayton copula density 225
7.5.2 Derivation of a 4-variate Frank copula density 226
7.5.3 Correlated default times 227
7.5.4 Variance–covariance robust estimation 228
7.5.5 Interest rates and foreign exchange rates in the analysis 229
8 Option Pricing with Copulas 231
8.1 Introduction 231
8.2 Pricing bivariate options in complete markets 232
8.2.1 Copula pricing kernels 232
8.2.2 Alternative pricing techniques 235
8.3 Pricing bivariate options in incomplete markets 239
8.3.1 Fr´echet pricing: super-replication in two dimensions 240
8.3.2 Copula pricing kernel 241
8.4 Pricing vulnerable options 243
8.4.1 Vulnerable digital options 244
8.4.2 Pricing vulnerable call options 246
8.4.3 Pricing vulnerable put options 248
8.4.4 Pricing vulnerable options in practice 250
8.5 Pricing rainbow two-color options 253
8.5.1 Call option on the minimum of two assets 254
8.5.2 Call option on the maximum of two assets 257
8.5.3 Put option on the maximum of two assets 258
8.5.4 Put option on the minimum of two assets 261
8.5.5 Option to exchange 262
8.5.6 Pricing and hedging rainbows with smiles: Everest notes 263
8.6 Pricing barrier options 267
8.6.1 Pricing call barrier options with copulas: the general framework 268
Contents ix
8.6.2 Pricing put barrier option: the general framework 270
8.6.3 Specifying the trigger event 272
8.6.4 Calibrating the dependence structure 276
8.6.5 The reflection copula 276
8.7 Pricing multivariate options: Monte Carlo methods 278
8.7.1 Application: basket option 279
Bibliography 281
Index 289 
【书评】  以下为【原创书评】

       简单来说，Copula是多个随机变量相关性的非线性度量，是我们常见的相关系数的一种推广。她使得我们能够对随机变量的相关性有更深入的了解。而金融中的量大多是随机变量。简单的股票价格，外汇比率，期货、期权的价格等等无一不是随机的。那么，在偌大的金融市场中，他们的相关性如何呢？股票A的价格波动如何影响10月份到期的小麦期货价格？如果一家上市公司出现了亏损，股票A的价格会如何变化？等等这些问题归根到底都是对相关性大小的描述。

       传统意义上我们使用相关系数来描述这种相关性。可是这就有一些问题：比如说，我们取随机变量X服从（0，1）上的均匀分布，然后构造A=X,B=2X；构造C=X,D=X^2.简单的计算我们发现cov(A,B)=1,cov(C,D)=1/3.这个结果是有意思的，因为A,B在（0，1）上完全正相关，而C,D也是完全正相关啊！我们的老师告诉我们，他们的相关系数不同是由于相关系数只能描述线性的相关关系。这就有意思了，在cov（）的概念下A,B 之间的相关关系要强于C,D的。可是，我们的市场中可不管线不线性啊！

      这时候，Copula就体现出了他的优越性！

      根据书中的介绍可以分别计算A,B ;C,D之间的Copula，我们会发现Copula(A,B)=Copula(C,D)=Frechet上界！而Frechet上界表示的正是完全正相关！

      通过上述的简单介绍你会发现Copula的用处，而实际上Copula也是70年代末才开始兴起的理论！到今天也是方兴未艾！将这种先进的方法引入金融领域正是这本书的成功之处！

      我是金融工程的学生，这本书是导师推荐的必读之书！书中的数学的确是多了一点，可这并不妨碍数学不好的同学阅读。因为那些证明你就算不看也不会影响对例子的了解和对理论的使用！书中的例子不算很多，可是非常经典。从BS模型到特殊期权的定价应有尽有！这绝对是一本不可错过的好书！

[此贴子已经被作者于2008-3-10 20:51:16编辑过]

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关键词：Methods Finance Copula Financ Method Finance Methods John Copula Wiley

这的确是一本非常棒的书！

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这么好的书，降价了！原来是30金，降为10金！

鼓励大家学习 Copula！

下不下来

我急需它呀，为什么我有10金却下不下来，我的神那！！

不会啊

我刚才刚试过，可以下载的

另外，我看到的已购买用户里面没有你的，所以...再试试？？

楼主你好，我刚买了你的这本好书，不过确实下载不下来（下到一半时就不行了，显示超时），希望你能把它发到我的邮箱里：apo_z@sohu.com   另外，也希望你也能不吝把你的 Monte Carlo Methods in Finance 这本书一并传给我。 我已经尽力买你的书里  可毕竟现在财力有限   眼看就快要到负分了  却真不敢想象你那30分我不知道什么时候能买得起   但看到好书确实眼馋  相信楼主也能明白其中苦衷  兄弟多谢了..........

好书，谢谢！

好东西，顶一下