本书建立了实务和理论的桥梁，主要讲述了期货市场的运作机制、采用期货的对冲策略、远期及期货价格的确定、期权市场的运作过程、雇员股票期权的性质、期权交易策略以及信用衍生产品、布莱克-斯科尔斯-默顿模型、希腊值及其运用等。书中尽量少采用数学知识，对如何使用数学的处理尤其谨慎，尽量避免使用一些令初学读者反感的带有许多上、下角标或函数变量的数学符号。同时，本书提供了大量的业界事例，使本书内容既贴近现实又丰富有趣。此外，本书还仔细解释了对许多读者而言有可能是新的概念，并针对这些概念给出了许多数值计算例子。
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有时连我自己都难以相信本书的第1版只有13章，篇幅只有330页！我必须不断地扩充本书的内容来跟上衍生产品市场的迅速发展趋势。
与本书的前几版类似，这一版可作为经济学、金融数学以及金融工程专业的研究生教材，也可以作为高年级中具有较好定量数学背景的本科生教材，此外本书对从事衍生产品市场交易的从业人员而言也是一本非常有用的参考书。令我欣慰的是本书的销售在从业人员中与在大学教材市场中同样好。
执笔衍生产品的作者必须做出一个有关数学运用程度的关键性决策。如果书中运用的数学难度太大，那么许多学生和从业人员会认为内容难以理解；反之，如果书中运用的数学难度太小，那么对许多重要问题的讨论会不可避免地停留在非常浅显的水平上。因此在写作中，我对书中如何使用数学的处理尤其谨慎，尽量避免使用一些令初学读者反感的带有许多上、下角标或函数变量的数学符号。一些非关键的数学内容要么省略了，要么放在了我的网站上或每章章末的附录中，也有一些其他内容可以在我的网站上获得。我详细解释了对许多读者而言有可能是新的概念，并针对这些概念给出了许多数值计算例子。
作为学习衍生产品的书，本书既可用于入门课程，也可用于高等课程。根据学生的不同背景，教师在课堂上可以以多种形式应用本书。讲授入门课程的教师可以侧重本书的前半部分内容，讲授高等课程的教师可以将后半部分的章节进行不同的组合。另外，我发现第37章的内容无论是对于入门课程还是高等课程而言都十分有益。
第10版新增的内容
相对第9版，在新版中很多内容都有所更新和改进。本书通篇采用隔夜指数互换（OIS）贴现，这种做法使本书内容更加顺畅，并且在理论上也更加严谨。对于像互换和利率远期合约这样的产品定价需要：①计算确定现金流数量的远期利率；②确定贴现的零息利率曲线（通常是OIS零息曲线）。这一方法可以推广到支付的现金流与任何风险利率有关的情形。
第10版的更新内容包括：
（1）重写了互换一章（第7章），陈述方式反映了市场实践的变化。
（2）新增了第9章，这一章涉及各种价值调节（CVA、DVA、FVA、MVA以及KVA）。虽然金融经济学家对FVA、MVA和KVA持有不同的看法（在本书中将会解释），但价值调节已经成为衍生产品定价的重要组成部分，因此有必要在本书中讨论这些内容。
（3）多个地方讨论了在定价中如何处理负利率。在对衍生产品定价时，在我们假设的无套利世界里，负利率毫无意义，但负利率在某些欧洲国家以及日本市场已经出现，因此负利率现象不可忽视。
（4）新增了一章（第31章），涉及利率结构的平衡模型，这些模型对于教学尤其重要，并且广泛使用在长期利率情形分析中。我决定将这些内容汇集在单独的一章中。
（5）增加了对计算希腊值和波动率微笑动态系统的细节。
（6）为了反映预期亏空和压力风险测度在监管以及风险管理中的重要性，增加了关于预期亏空和压力风险测度的讨论。
（7）加入了SABR模型。
（8）更新了中央交易对手（CCP）和场外衍生产品监管的内容。
（9）完善了关于鞅、计价单位、尾随对冲、票息剥离法和可转债的讨论。
（10）为了反映市场变化，对例子进行了更新。
（11）在每章末尾增加了一些新的习题，也对原来的习题进行了更新。
（12）更新了DerivaGem软件。
软件
本书包括DerivaGem软件的第4.00版，这一软件包括两个Excel的应用：期权计算器（Options Calculator）及应用工具（Applications Builder）。期权计算器包括一个易于应用的软件，用户可以利用这些软件来对多类不同形式的期权进行定价。应用工具中包括若干Excel函数，用户可以在这些函数的基础上研发自身的应用程序，应用工具包括若干应用样本，通过这些样本应用，学生可以更容易地探讨期权的性质与不同的数值计算方法。教师可以采用应用工具来设计出更有趣的作业题。
DerivaGem 4.00软件包括许多新模型（Heston、SABR、巴舍利耶正态模型和偏移对数正态），用于产品定价。本书的最后有关于这一软件更详尽的说明，用户可以在我的网站www-2.rotman.utoronto.ca/~hull上下载此软件。
幻灯片
在培生教师资源中心或者我的网站中存有上百页关于本书的幻灯片，欢迎采用本书的教师将这些幻灯片用于教学。
问题解答
每章最后的习题分为练习题和作业题两组，培生公司出版的Options，Futures，and Other Derivatives 10e：Solution Manual（ISBN-10：013462999X）手册给出了练习题的答案，学生可以购买这一手册。
教师手册
选用本书的教师可以通过在线的形式从培生公司来获得教师手册，这一手册包含了所有问题的答案（包括练习题和作业题），同时也含有每章的讲义、题库习题、课程组织心得和一些相关的Excel计算表。一
技术报告
书中的某些观点是通过技术报告（Technical Notes）来说明的。读者可以在我的网站www-2.rotman.utoronto.ca/~hull/TechnicalNotes上下载这些技术报告。
在本书中，我没有包括这些技术报告，这是为了能够更好地组织材料，以保证学生更好地理解所讲述的内容。
鸣谢
在本书的写作过程中，许多人提供了帮助。事实上，如果一一列举所有给过本书建议的人，那所占的篇幅就太长了。在这里我想强调，我特别受益于许多使用本书授课的学术界同人的建议以及金融从业人员的评论。感谢多伦多大学听我授课的学生，他们给本书提供了许多非常好的建议。Geometric出版社的Eddie Mizzi对本书终稿的编辑和装订做了很出色的工作。罗马国际社会科学自由大学（Luiss Guido Carli University in Rome）的Emilio Barone为本书提供了许多详尽的建议。
我要特别感谢艾伦·怀特（Alan White），艾伦是我在多伦多大学的同事，在过去的30多年里，艾伦和我在衍生产品与风险管理领域有许多合作研究。在这期间，我们花了大量的时间在一些关键领域进行探讨。本书所采用的许多新观点以及对一些旧观点的新解释方法是艾伦和我共同拥有的。另外，艾伦也是DerivaGem软件的主要开发者。
我要特别感谢培生公司的多位工作人员，特别是Donna Battista、Neeraj Bhalla、Nicole Suddeth和Alison Kalil，我在此感谢他们对我的热情帮助、建议以及鼓励。
我在此欢迎读者对本书提出建议，我的E-mail地址是：hull@rotman.utoronto.ca。
约翰·赫尔（John C. Hull）
金融投资
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目 录
出版说明
技术报告
前 言
作者简介
术 语 表
第1章 导论 / 1
1.1 交易所市场 / 2
1.2 场外交易市场 / 3
1.3 远期合约 / 6
1.4 期货合约 / 8
1.5 期权 / 8
1.6 交易员的类型 / 11
1.7 对冲者 / 11
1.8 投机者 / 14
1.9 套利者 / 16
1.10 危险 / 17
小结 / 18
推荐阅读 / 19
练习题 / 19
作业题 / 21
第2章 期货市场与中央交易对手 / 24
2.1 背景知识 / 24
2.2 期货合约的规格 / 26
2.3 期货价格收敛到即期价格 / 28
2.4 保证金账户的运作 / 29
2.5 场外市场 / 32
2.6 市场报价 / 36
2.7 交割 / 38
2.8 交易员类型和交易指令类型 / 39
2.9 制度 / 40
2.10 会计和税收 / 41
2.11 远期与期货合约的比较 / 43
小结 / 44
推荐阅读 / 45
练习题 / 45
作业题 / 47
第3章 利用期货的对冲策略 / 49
3.1 基本原理 / 49
3.2 拥护与反对对冲的观点 / 51
3.3 基差风险 / 54
3.4 交叉对冲 / 58
3.5 股指期货 / 62
3.6 向前滚动对冲 / 68
小结 / 70
推荐阅读 / 70
练习题 / 71
作业题 / 73
附录3A 资本资产定价模型 / 75
第4章 利率 / 77
4.1 利率的种类 / 77
4.2 互换利率 / 79
4.3 无风险利率 / 80
4.4 利率的度量 / 81
4.5 零息利率 / 84
4.6 债券定价 / 84
4.7 确定零息利率 / 85
4.8 远期利率 / 89
4.9 远期利率合约 / 92
4.10 久期 / 94
4.11 凸性 / 98
4.12 利率期限结构理论 / 99
小结 / 101
推荐阅读 / 102
练习题 / 102
作业题 / 105
第5章 确定远期和期货价格 / 107
5.1 投资资产与消费资产 / 107
5.2 卖空交易 / 108
5.3 假设与符号 / 109
5.4 投资资产的远期价格 / 110
5.5 提供已知中间收入的资产 / 113
5.6 收益率为已知的情形 / 115
5.7 远期合约定价 / 115
5.8 远期和期货价格相等吗 / 117
5.9 股指期货价格 / 118
5.10 货币上的远期和期货合约 / 120
5.11 商品期货 / 124
5.12 持有成本 / 126
5.13 交割选择 / 127
5.14 期货价格与预期未来即期价格 / 127
小结 / 130
推荐阅读 / 131
练习题 / 131
作业题 / 133
第6章 利率期货 / 135
6.1 天数计算和报价惯例 / 135
6.2 美国国债期货 / 138
6.3 欧洲美元期货 / 143
6.4 基于久期的期货对冲策略 / 148
6.5 对于资产与负债组合的对冲 / 150
小结 / 150
推荐阅读 / 151
练习题 / 151
作业题 / 153
第7章 互换 / 155
7.1 互换合约的机制 / 156
7.2 天数计算惯例 / 161
7.3 确认书 / 162
7.4 相对优势的观点 / 162
7.5 利率互换定价 / 165
7.6 互换价值随时间的变化 / 168
7.7 固定利息与固定利息货币互换 / 169
7.8 货币互换定价 / 172
7.9 其他货币互换 / 174
7.10 信用风险 / 175
7.11 信用违约互换 / 176
7.12 其他类型的互换 / 177
小结 / 179
推荐阅读 / 179
练习题 / 179
作业题 / 182
第8章 证券化与2007年信用危机 / 184
8.1 证券化 / 184
8.2 美国住房市场 / 188
8.3 问题出在哪里 / 192
8.4 危机的后果 / 194
小结 / 195
推荐阅读 / 196
练习题 / 197
作业题 / 197
第9章 价值调节量 / 199
9.1 CVA和DVA / 199
9.2 FVA和MVA / 202
9.3 KVA / 205
9.4 计算问题 / 206
小结 / 207
推荐阅读 / 207
练习题 / 208
作业题 / 208
第10章 期权市场机制 / 209
10.1 期权类型 / 209
10.2 期权头寸 / 211
10.3 标的资产 / 213
10.4 股票期权的细节 / 215
10.5 交易 / 219
10.6 佣金 / 220
10.7 保证金 / 221
10.8 期权结算公司 / 222
10.9 监管制度 / 223
10.10 税收 / 223
10.11 认股权证、雇员股票期权和可转换债券 / 225
10.12 场外市场 / 226
小结 / 226
推荐阅读 / 227
练习题 / 227
作业题 / 229
第11章 股票期权的性质 / 231
11.1 影响期权价格的因素 / 231
11.2 假设与记号 / 235
11.3 期权价格的上限与下限 / 236
11.4 看跌–看涨平价关系式 / 238
11.5 无股息股票上的看涨期权 / 241
11.6 无股息股票上的看跌期权 / 244
11.7 股息对期权的影响 / 246
小结 / 247
推荐阅读 / 248
练习题 / 248
作业题 / 250
第12章 期权交易策略 / 252
12.1 保本债券 / 252
12.2 交易单一期权与股票的策略 / 254
12.3 差价 / 256
12.4 组合 / 264
12.5 具有其他收益形式的组合 / 267
小结 / 268
推荐阅读 / 269
练习题 / 269
作业题 / 270
第13章 二叉树 / 272
13.1 单步二叉树模型与无套利方法 / 272
13.2 风险中性定价 / 276
13.3 两步二叉树 / 278
13.4 看跌期权的例子 / 281
13.5 美式期权 / 282
13.6 delta / 283
13.7 选取u和d使二叉树与波动率吻合 / 284
13.8 二叉树公式 / 286
13.9 增加二叉树的步数 / 286
13.10 使用DerivaGem软件 / 287
13.11 其他标的资产上的期权 / 288
小结 / 291
推荐阅读 / 292
练习题 / 293
作业题 / 294
附录13A 由二叉树模型推导布莱克–斯科尔斯–默顿期权定价公式 / 296
第14章 维纳过程和伊藤引理 / 300
14.1 马尔可夫性质 / 300
14.2 连续时间随机过程 / 301
14.3 描述股票价格的过程 / 306
14.4 参数 / 309
14.5 相关过程 / 310
14.6 伊藤引理 / 311
14.7 对数正态分布的性质 / 312
小结 / 313
推荐阅读 / 314
练习题 / 314
作业题 / 315
附录14A 伊藤引理的非严格推导 / 317
第15章 布莱克–斯科尔斯–默顿模型 / 319
15.1 股票价格的对数正态分布性质 / 320
15.2 收益率的分布 / 321
15.3 期望收益 / 322
15.4 波动率 / 323
15.5 布莱克–斯科尔斯–默顿微分方程的概念 / 327
15.6 布莱克–斯科尔斯–默顿微分方程的推导 / 329
15.7 风险中性定价 / 332
15.8 布莱克–斯科尔斯–默顿定价公式 / 333
15.9 累积正态分布函数 / 336
15.10 权证与雇员股票期权 / 337
15.11 隐含波动率 / 339
15.12 股息 / 341
小结 / 344
推荐阅读 / 345
练习题 / 346
作业题 / 348
附录15A 布莱克–斯科尔斯–默顿公式的证明 / 350
第16章 雇员股票期权 / 352
16.1 合约的设计 / 352
16.2 期权会促进股东与管理人员的利益一致吗 / 354
16.3 会计问题 / 355
16.4 定价 / 356
16.5 倒填日期丑闻 / 361
小结 / 362
推荐阅读 / 362
练习题 / 362
作业题 / 363
第17章 股指期权与货币期权 / 365
17.1 股指期权 / 365
17.2 货币期权 / 367
17.3 支付已知连续股息率的股票期权 / 370
17.4 欧式股指期权的定价 / 372
17.5 欧式货币期权的定价 / 375
17.6 美式期权 / 376
小结 / 377
推荐阅读 / 377
练习题 / 378
作业题 / 380
第18章 期货期权与布莱克模型 / 381
18.1 期货期权的特性 / 381
18.2 期货期权被广泛应用的原因 / 384
18.3 欧式即期期权和欧式期货期权 / 384
18.4 看跌–看涨平价关系式 / 385
18.5 期货期权的下限 / 386
18.6 期货价格在风险中性世界的漂移率 / 387
18.7 期货期权定价的布莱克模型 / 388
18.8 由布莱克模型代替布莱克–斯科尔斯–默顿模型 / 389
18.9 采用二叉树对期货期权定价 / 390
18.10 美式期货期权与美式即期期权 / 392
18.11 期货式期权 / 393
小结 / 393
推荐阅读 / 394
练习题 / 394
作业题 / 396
第19章 希腊值 / 397
19.1 例解 / 397
19.2 裸露头寸和带保头寸 / 398
19.3 希腊值的计算 / 400
19.4 delta对冲 / 401
19.5 theta / 407
19.6 gamma / 409
19.7 delta、theta和gamma之间的关系 / 413
19.8 vega / 414
19.9 rho / 416
19.10 对冲的现实性 / 417
19.11 情景分析 / 417
19.12 公式的推广 / 419
19.13 资产组合保险 / 421
19.14 股票市场波动率 / 423
小结 / 423
推荐阅读 / 425
练习题 / 425
作业题 / 427
附录19A 泰勒级数展开和对冲参数 / 429
第20章 波动率微笑 / 430
20.1 为什么波动率微笑对看涨期权与看跌期权是一样的 / 430
20.2 货币期权 / 432
20.3 股票期权 / 435
20.4 其他刻画波动率微笑的方法 / 437
20.5 波动率期限结构与波动率曲面 / 437
20.6 最小方差delta / 439
20.7 模型的作用 / 439
20.8 当预计有大幅度价格跳跃时 / 440
小结 / 441
推荐阅读 / 442
练习题 / 443
作业题 / 444
附录20A 由波动率微笑确定隐含风险中性分布 / 446
第21章 基本数值方法 / 449
21.1 二叉树 / 449
21.2 利用二叉树对股指、货币与期货合约上的期权定价 / 457
21.3 支付股息股票的二叉树模型 / 459
21.4 构造树形的其他方法 / 464
21.5 依赖时间的参数 / 467
21.6 蒙特卡罗模拟法 / 468
21.7 方差缩减程序 / 474
21.8 有限差分法 / 477
小结 / 487
推荐阅读 / 488
练习题 / 489
作业题 / 491
第22章 在险价值与预期亏损 / 493
22.1 VaR与ES测度 / 493
22.2 历史模拟法 / 496
22.3 模型构建法 / 500
22.4 线性模型 / 503
22.5 二次模型 / 508
22.6 蒙特卡罗模拟法 / 511
22.7 不同方法的比较 / 512
22.8 回顾测试 / 512
22.9 主成分分析法 / 513
小结 / 516
推荐阅读 / 517
练习题 / 517
作业题 / 518
第23章 估计波动率和相关系数 / 520
23.1 估计波动率 / 520
23.2 指数加权移动平均模型 / 522
23.3 GARCH（1，1）模型 / 524
23.4 模型选择 / 525
23.5 极大似然估计法 / 526
23.6 利用GARCH（1，1）模型预测波动率 / 531
23.7 相关系数 / 534
23.8 将EWMA应用于4个指数的例子 / 537
小结 / 539
推荐阅读 / 539
练习题 / 539
作业题 / 541
第24章 信用风险 / 543
24.1 信用评级 / 543
24.2 历史违约概率 / 544
24.3 回收率 / 545
24.4 由债券收益率溢差估计违约概率 / 546
24.5 违约概率估计的比较 / 549
24.6 利用股价估计违约概率 / 552
24.7 衍生产品交易中的信用风险 / 554
24.8 违约相关性 / 560
24.9 信用VaR / 563
小结 / 565
推荐阅读 / 565
练习题 / 566
作业题 / 568
第25章 信用衍生产品 / 569
25.1 信用违约互换 / 570
25.2 CDS定价 / 573
25.3 信用指数 / 577
25.4 固定券息的使用 / 578
25.5 CDS远期合约与期权 / 579
25.6 篮筐式CDS / 579
25.7 总收益互换 / 579
25.8 债务抵押债券 / 581
25.9 相关系数在篮筐式CDS与CDO中的作用 / 583
25.10 合成CDO的定价 / 583
25.11 其他模型 / 590
小结 / 592
推荐阅读 / 592
练习题 / 593
作业题 / 594
第26章 奇异期权 / 596
26.1 组合期权 / 596
26.2 永续美式看涨与看跌期权 / 597
26.3 非标准美式期权 / 598
26.4 缺口期权 / 599
26.5 远期开始期权 / 600
26.6 棘轮期权 / 600
26.7 复合期权 / 600
26.8 选择人期权 / 601
26.9 障碍期权 / 602
26.10 二元式期权 / 604
26.11 回望期权 / 605
26.12 喊价式期权 / 607
26.13 亚式期权 / 608
26.14 资产交换期权 / 609
26.15 涉及多种资产的期权 / 610
26.16 波动率和方差互换 / 611
26.17 静态期权复制 / 614
小结 / 616
推荐阅读 / 617
练习题 / 617
作业题 / 619
第27章 再谈模型和数值算法 / 622
27.1 布莱克–斯科尔斯–默顿的替代模型 / 623
27.2 随机波动率模型 / 628
27.3 IVF模型 / 630
27.4 可转换证券 / 632
27.5 路径依赖型衍生产品 / 634
27.6 障碍期权 / 637
27.7 两个相关资产上的期权 / 640
27.8 蒙特卡罗模拟法与美式期权 / 642
小结 / 646
推荐阅读 / 647
练习题 / 648
作业题 / 650
第28章 鞅与测度 / 652
28.1 风险市场价格 / 653
28.2 多个状态变量 / 656
28.3 鞅 / 657
28.4 计价单位的其他选择 / 658
28.5 多个因子情形下的推广 / 661
28.6 改进布莱克模型 / 662
28.7 资产交换期权 / 663
28.8 计价单位变换 / 664
小结 / 666
推荐阅读 / 667
练习题 / 667
作业题 / 668
第29章 利率衍生产品：标准市场模型 / 670
29.1 债券期权 / 670
29.2 利率上限和下限 / 675
29.3 欧式利率互换期权 / 681
29.4 利率衍生产品的对冲 / 684
小结 / 685
推荐阅读 / 686
练习题 / 686
作业题 / 688
第30章 凸性、时间与Quanto调整 / 689
30.1 凸性调整 / 689
30.2 时间调整 / 693
30.3 Quanto / 695
小结 / 698
推荐阅读 / 698
练习题 / 698
作业题 / 700
附录30A 凸性调整公式的证明 / 701
第31章 短期利率均衡模型 / 702
31.1 背景 / 702
31.2 单因子模型 / 704
31.3 现实世界与风险中性世界 / 709
31.4 参数估计 / 710
31.5 更复杂的模型 / 711
小结 / 712
推荐阅读 / 712
练习题 / 712
作业题 / 713
第32章 短期利率无套利模型 / 715
32.1 均衡模型的推广 / 715
32.2 债券期权 / 719
32.3 波动率结构 / 720
32.4 利率树形 / 721
32.5 建立树形的步骤 / 723
32.6 校正 / 732
32.7 利用单因子模型进行对冲 / 734
小结 / 735
推荐阅读 / 735
练习题 / 735
作业题 / 736
第33章 HJM模型、LMM以及多种零息曲线 / 738
33.1 HJM模型 / 738
33.2 LMM / 741
33.3 对多种零息曲线的处理方法 / 751
33.4 联邦机构住房抵押证券 / 752
小结 / 754
推荐阅读 / 755
练习题 / 755
作业题 / 756
第34章 再谈互换 / 757
34.1 标准交易的变形 / 757
34.2 复合互换 / 759
34.3 货币互换 / 760
34.4 更复杂的互换 / 761
34.5 股权互换 / 764
34.6 具有内含期权的互换 / 765
34.7 其他互换 / 768
小结 / 769
推荐阅读 / 770
练习题 / 770
作业题 / 770
第35章 能源与商品衍生产品 / 772
35.1 农产品 / 772
35.2 金属 / 773
35.3 能源产品 / 774
35.4 商品价格模型 / 776
35.5 气候衍生产品 / 782
35.6 保险衍生产品 / 783
35.7 气候与保险衍生产品定价 / 784
35.8 能源生产商如何对冲风险 / 785
小结 / 786
推荐阅读 / 786
练习题 / 787
作业题 / 788
第36章 实物期权 / 789
36.1 资本投资评估 / 789
36.2 风险中性定价的推广 / 790
36.3 估计风险市场价格 / 792
36.4 商业估价中的应用 / 793
36.5 投资机会中期权的定价 / 793
小结 / 800
推荐阅读 / 800
练习题 / 801
作业题 / 801
第37章 衍生产品重大金融损失与借鉴 / 803
37.1 所有衍生产品使用者的教训 / 803
37.2 对于金融机构的教训 / 807
37.3 对于非金融机构的教训 / 812
小结 / 814
推荐阅读 / 814
附录A DerivaGem软件 / 815
附录B 世界上的主要期权期货交易所 / 820
附录C 当x≤0时N（x）的取值 / 821
附录D 当x≥0时N（x）的取值 / 822
Contents in Brief
List of Technical Notes
Preface
About the Author
1.Introduction...................................................................................................1
2.Futures markets and central counterparties.......................................................24
3.Hedging strategies using futures......................................................................49
4.Interest rates................................................................................................77
5.Determination of forward and futures prices...................................................107
6.Interest rate futures.....................................................................................135
7.Swaps.......................................................................................................155
8.Securitization and the credit crisis of 2007......................................................184
9.XVAs........................................................................................................199
10.Mechanics of options markets......................................................................209
11.Properties of stock options...........................................................................231
12.Trading strategies involving options...............................................................252
13.Binomial trees............................................................................................272
14.Wiener processes and I t魭s l emma.................................................................300
15.The Black朣choles朚erton model................................................................319
16.Employee stock options...............................................................................352
17.Options on stock indices and currencies.........................................................365
18.Futures options and Black抯 model................................................................381
19.The Greek letters........................................................................................397
20.Volatility smiles..........................................................................................430
21.Basic numerical procedures..........................................................................449
22.Value at risk and expected shortfall...............................................................493
23.Estimating volatilities and correlations...........................................................520
24.Credit risk.................................................................................................543
25.Credit derivatives........................................................................................569
26.Exotic options............................................................................................596
27.More on models and numerical procedures.....................................................622
28.Martingales and measures............................................................................652
29.Interest rate derivatives: The standard market models.......................................670
30.Convexity, timing, and quanto adjustments.....................................................689
31.Equilibrium models of the short rate.............................................................702
32.No-arbitrage models of the short rate............................................................715
33.HJM, LMM, and multiple zero curves...........................................................738
34.Swaps Revisited..........................................................................................757
35.Energy and commodity derivatives................................................................772
36.Real options..............................................................................................789
37.Derivatives mishaps and what we can learn from them.....................................803
A. DerivaGem software...............................................................................815
B. Major exchanges trading futures and options...............................................................................820
C. Table for N(x) when x0...............................................................................821
D. Table for N(x) when x0...............................................................................822
Contents
List of Technical Notes
Preface
Preface
About the Author
Chapter1.Introduction....................................................................................................1
1.1 Exchange-traded markets........................................................................2
1.2 Over-the-counter markets........................................................................3
1.3 Forward contracts..................................................................................6
1.4 Futures contracts...................................................................................8
1.5 Options................................................................................................8
1.6 Types of traders...................................................................................11
1.7 Hedgers..............................................................................................11
1.8 Speculators.........................................................................................14
1.9 Arbitrageurs........................................................................................16
1.10 Dangers.............................................................................................17
Summary............................................................................................18
Further reading...................................................................................19
Practice questions.................................................................................19
Further questions.................................................................................21
Chapter2.Futures markets and central counterparties.........................................................24
2.1 Background........................................................................................24
2.2 Specication of a futures contract...........................................................26
2.3 Convergence of futures price to spot price...............................................28
2.4 The operation of margin accounts..........................................................29
2.5 OTC markets......................................................................................32
2.6 Market quotes.....................................................................................36
2.7 Delivery.............................................................................................38
2.8 Types of traders and types of orders.......................................................39
2.9 Regulation..........................................................................................40
2.10 Accounting and tax..............................................................................41
2.11 Forward vs. futures contracts.................................................................43
Summary............................................................................................44
Further reading...................................................................................45
Practice questions.................................................................................45
Further questions.................................................................................47
Chapter3. Hedging strategies using futures........................................................................49
3.1 Basic principles....................................................................................49
3.2 Arguments for and against hedging........................................................51
3.3 Basis risk............................................................................................54
3.4 Cross hedging.....................................................................................58
3.5 Stock index futures...............................................................................62
3.6 Stack and roll......................................................................................68
Summary............................................................................................70
Further reading....................................................................................70
Practice questions.................................................................................71
Further questions.................................................................................73
Appendix: Capital asset pricing model....................................................75
Chapter4. Interest rates.................................................................................................77
4.1 Types of rates......................................................................................77
4.2 Swap rates...........................................................................................79
4.3 The risk-free rate..................................................................................80
4.4 Measuring interest rates........................................................................81
4.5 Zero rates...........................................................................................84
4.6 Bond pricing.......................................................................................84
4.7 Determining zero rates..........................................................................85
4.8 Forward rates......................................................................................89
4.9 Forward rate agreements.......................................................................92
4.10 Duration.............................................................................................94
4.11 Convexity............................................................................................98
4.12 Theories of the term structure of interest rates..........................................99
Summary..........................................................................................101
Further reading..................................................................................102
Practice questions...............................................................................102
Further questions...............................................................................105
Chapter5. Determination of forward and futures prices......................................................107
5.1 Investment assets vs. consumption assets...............................................107
5.2 Short selling......................................................................................108
5.3 Assumptions and notation...................................................................109
5.4 Forward price for an investment asset...................................................110
5.5 Known income..................................................................................113
5.6 Known yield......................................................................................115
5.7 Valuing forward contracts...................................................................115
5.8 Are forward prices and futures prices equal?..........................................117
5.9 Futures prices of stock indices..............................................................118
5.10 Forward and futures contracts on currencies..........................................120
5.11 Futures on commodities......................................................................124
5.12 The cost of carry................................................................................126
5.13 Delivery options.................................................................................127
5.14 Futures prices and expected future spot prices........................................127
Summary..........................................................................................130
Further reading..................................................................................131
Practice questions...............................................................................131
Further questions...............................................................................133
Chapter6. Interest rate futures......................................................................................135
6.1 Day count and quotation conventions...................................................135
6.2 Treasury bond futures.........................................................................138
6.3 Eurodollar futures..............................................................................143
6.4 Duration-based hedging strategies using futures......................................148
6.5 Hedging portfolios of assets and liabilities.............................................150
Summary..........................................................................................150
Further reading..................................................................................151
Practice questions................................................................................151
Further questions................................................................................153
Chapter7. Swaps.........................................................................................................155
7.1 Mechanics of interest rates waps...........................................................156
7.2 Day count issues.................................................................................161
7.3 Conrmations....................................................................................162
7.4 The comparative-advantage argument....................................................162
7.5 Valuation of interest rates waps.............................................................165
7.6 How the value changes through time.....................................................168
7.7 Fixed-for-xed currencys waps..............................................................169
7.8 Valuation of xed-for-xed currencys waps.............................................172
7.9 Other currency swaps..........................................................................174
7.10 Credit risk.........................................................................................175
7.11 Credit default swaps............................................................................176
7.12 Other types of swaps...........................................................................177
Summary...........................................................................................179
Further reading..................................................................................179
Practice questions................................................................................179
Further questions................................................................................182
Chapter8. Securitization and the credit crisis of 2007........................................................184
8.1 Securitization.....................................................................................184
8.2 The U.S. housing market.....................................................................188
8.3 What went wrong?..............................................................................192
8.4 The aftermath....................................................................................194
Summary...........................................................................................195
Further reading..................................................................................196
Practice questions................................................................................197
Further questions................................................................................197
Chapter9.XVAs.........................................................................................................199
9.1 CVA and DVA...................................................................................199
9.2 FVA and MVA..................................................................................202
9.3 KVA.................................................................................................205
9.4 Calculation issues...............................................................................206
Summary...........................................................................................207
Further reading..................................................................................207
Practice questions................................................................................208
Further questions................................................................................208
Chapter10. Mechanics of options markets.........................................................................209
10.1 Types of options.................................................................................209
10.2 Option positions.................................................................................211
10.3 Underlying assets................................................................................213
10.4 Specication of stock options...............................................................215
10.5 Trading.............................................................................................219
10.6 Commissions......................................................................................220
10.7 Margin requirements...........................................................................221
10.8 The options clearing corporation...........................................................222
10.9 Regulation.........................................................................................223
10.10 Taxation............................................................................................223
10.11 Warrants, employee stock options, and convertibles.................................225
10.12 Over-the-counter options markets..........................................................226
Summary...........................................................................................226
Further reading..................................................................................227
Practice questions...............................................................................227
Further questions...............................................................................229
Chapter11. Properties of stock options.............................................................................231
11.1 Factors affecting option prices..............................................................231
11.2 Assumptions and notation...................................................................235
11.3 Upper and lower bounds for option prices.............................................236
11.4 Put朿all parity...................................................................................238
11.5 Calls on a non-dividend-paying stock....................................................241
11.6 Puts on a non-dividend-paying stock.....................................................244
11.7 Effect of dividends.............................................................................246
Summary..........................................................................................247
Further reading..................................................................................248
Practice questions...............................................................................248
Further questions...............................................................................250
Chapter12. Trading strategies involving options..................................................................252
12.1 Principal-protected notes.....................................................................252
12.2 Trading an option and the underlying asset...........................................254
12.3 Spreads.............................................................................................256
12.4 Combinations....................................................................................264
12.5 Other payoffs.....................................................................................267
Summary..........................................................................................268
Further reading..................................................................................269
Practice questions...............................................................................269
Further questions...............................................................................270
Chapter13. Binomial trees.............................................................................................272
13.1 A one-step binomial model and a no-arbitrage argument.........................272
13.2 Risk-neutral valuation.........................................................................276
13.3 Two-step binomial trees......................................................................278
13.4 A put example...................................................................................281
13.5 American options...............................................................................282
13.6 Delta................................................................................................283
13.7 Matching volatility with u and d..........................................................284
13.8 The binomial tree formulas..................................................................286
13.9 Increasing the number of steps.............................................................286
13.10 Using DerivaGem..............................................................................287
13.11 Options on other assets.......................................................................288
Summary..........................................................................................291
Further reading..................................................................................292
Practice questions...............................................................................293
Further questions...............................................................................294
Appendix: Derivation of the Black-Scholes-Merton option-pricing formula from a binomialt ree.......................296
Chapter14. Wiener processes and Ito's lemma...................................................................300
14.1 The Markov property.........................................................................300
14.2 Continuous-time stochastic processes.....................................................301
14.3 The process for a stock price...............................................................306
14.4 The parameters..................................................................................309
14.5 Correlated processes...........................................................................310
14.6 Ito垝s lemma.......................................................................................311
14.7 The lognormal property......................................................................312
Summary...........................................................................................313
Further reading..................................................................................314
Practice questions................................................................................314
Further questions................................................................................315
Appendix: A nonrigorous derivation of Ito垝s lemma.................................317
Chapter15. The Black-Scholes-Merton model..................................................................319
15.1 Lognormal property of stock prices.......................................................320
15.2 The distribution of the rate of return.....................................................321
15.3 The expected return.............................................................................322
15.4 Volatility...........................................................................................323
15.5 The idea underlying the Black-Scholes-Merton differential equation.........327
15.6 Derivation of the Black-Scholes-Merton differential equation..................329
15.7 Risk-neutral valuation.........................................................................332
15.8 Black-Scholes-Merton pricing formulas................................................333
15.9 Cumulative normal distribution function................................................336
15.10 Warrants and employee stock options....................................................337
15.11 Implied volatilities...............................................................................339
15.12 Dividends..........................................................................................341
Summary...........................................................................................344
Further reading..................................................................................345
Practice questions................................................................................346
Further questions................................................................................348
Appendix: Proof of Black-Scholes-Merton formula using risk-neutral valuation............................................................................350
Chapter16. Employee stock options..................................................................................352
16.1 Contractual arrangements.....................................................................352
16.2 Do options align the interests of shareholders and managers?....................354
16.3 Accounting issues...............................................................................355
16.4 Valuation...........................................................................................356
16.5 Backdating scandals............................................................................361
Summary...........................................................................................362
Further reading..................................................................................362
Practice questions................................................................................362
Further questions................................................................................363
Chapter17. Options on stockindices and currencies............................................................365
17.1 Options on stock indices......................................................................365
17.2 Currency options................................................................................367
17.3 Options on stocks paying known dividend yields.....................................370
17.4 Valuation of European stock index options.............................................372
17.5 Valuation of European currency options.................................................375
17.6 American options...............................................................................376
Summary...........................................................................................377
Further reading..................................................................................377
Practice questions................................................................................378
Further questions................................................................................380
Chapter18. Futures options and Black抯 model...................................................................381
18.1 Nature of futures options.....................................................................381
18.2 Reasons for the popularity of futures options.........................................384
18.3 European spot and futures options........................................................384
18.4 Put朿all parity...................................................................................385
18.5 Bounds for futures options...................................................................386
18.6 Drift of a futures prices in a risk-neutral world......................................387
18.7 Black's model for valuing futures options..............................................388
18.8 Using Black's model instead of Black-Scholes-Merton...........................389
18.9 Valuation of futures options using binomial trees....................................390
18.10 American futures options vs. American spot options...............................392
18.11 Futures-style options...........................................................................393
Summary..........................................................................................393
Further reading..................................................................................394
Practice questions...............................................................................394
Further questions...............................................................................396
Chapter19. The Greek letters.........................................................................................397
19.1 Illustration........................................................................................397
19.2 Naked and covered positions...............................................................398
19.3 Greek letter calculation.......................................................................400
19.4 Delta hedging....................................................................................401
19.5 Theta...............................................................................................407
19.6 Gamma............................................................................................409
19.7 Relationship between delta, theta, and gamma.......................................413
19.8 Vega................................................................................................414
19.9 Rho.................................................................................................416
19.10 The realities of hedging.......................................................................417
19.11 Scenario analysis................................................................................417
19.12 Extension of formulas.........................................................................419
19.13 Portfolio insurance.............................................................................421
19.14 Stock market volatility........................................................................423
Summary..........................................................................................423
Further reading..................................................................................425
Practice questions...............................................................................425
Further questions...............................................................................427
Appendix: Taylor series expansions and Greek letters..............................429
Chapter20. Volatility smiles...........................................................................................430
20.1 Why the volatility smile is the same for calls and puts.............................430
20.2 Foreign currency options.....................................................................432
20.3 Equity options...................................................................................435
20.4 Alternative ways of characterizing the volatility smile...............................437
20.5 The volatility term structure and volatility surfaces..................................437
20.6 Minimum variance delta.....................................................................439
20.7 The role of the model.........................................................................439
20.8 When a single large jump is anticipated.................................................440
Summary..........................................................................................441
Further reading..................................................................................442
Practice questions...............................................................................443
Further questions...............................................................................444
Appendix: Determin ingimplied risk-neutral distributions from volatility smiles...................................................................446
Chapter21. Basic numerical procedures............................................................................449
21.1 Binomial trees....................................................................................449
21.2 Using the binomial tree for options on indices, currencies, and futures contracts......................................................................................457
21.3 Binomial model for a dividend-paying stock...........................................459
21.4 Alternative procedures for constructing trees..........................................464
21.5 Time-dependent parameters..................................................................467
21.6 Monte Carlo simulation.......................................................................468
21.7 Variance reduction procedures..............................................................474
21.8 Finite difference methods.....................................................................477
Summary...........................................................................................487
Further reading..................................................................................488
Practice questions................................................................................489
Further questions................................................................................491
Chapter22. Value at risk and expected shortfall.................................................................493
22.1 The VaR and ES measures...................................................................493
22.2 Historical simulation...........................................................................496
22.3 Model-building approach.....................................................................500
22.4 The linear model................................................................................503
22.5 The quadratic model...........................................................................508
22.6 Monte Carlo simulation.......................................................................511
22.7 Comparison of approaches...................................................................512
22.8 Back testing.......................................................................................512
22.9 Principal components analysis...............................................................513
Summary...........................................................................................516
Further reading..................................................................................517
Practice questions................................................................................517
Further questions................................................................................518
Chapter23. Estimating volatilities and correlations..............................................................520
23.1 Estimating volatility............................................................................520
23.2 The exponentially weighted moving average model...................................522
23.3 The GARCH(1,1) model....................................................................524
23.4 Choosing between the models...............................................................525
23.5 Maximum likelihood methods...............................................................526
23.6 Using GARCH(1,1) to forecast future volatility.....................................531
23.7 Correlations.......................................................................................534
23.8 Application of EWMA to four-index example.........................................537
Summary...........................................................................................539
Further reading..................................................................................539
Practice questions................................................................................539
Further questions................................................................................541
Chapter24.Credit risk...................................................................................................543
24.1 Credit ratings.....................................................................................543
24.2 Historical default probabilities..............................................................544
24.3 Recovery rates....................................................................................545
24.4 Estimating default probabilities from bond yield spreads...........................546
24.5 Comparison of default probability estimates............................................549
24.6 Using equity prices to estimate default probabilities.................................552
24.7 Credit risk in derivatives transactions.....................................................554
24.8 Default correlation..............................................................................560
24.9 Credit VaR........................................................................................563
Summary...........................................................................................565
Further reading..................................................................................565
Practice questions................................................................................566
Further questions................................................................................568
Chapter25. Credit derivatives.........................................................................................569
25.1 Credit default swaps...........................................................................570
25.2 Valuation of credit default swaps..........................................................573
25.3 Credit indices....................................................................................577
25.4 The use of xed coupons.....................................................................578
25.5 CDS forwards and options..................................................................579
25.6 Basket credit default swaps..................................................................579
25.7 Total return swaps.............................................................................579
25.8 Collateralized debt obligations..............................................................581
25.9 Role of correlation in abasket CDS and CDO.......................................583
25.10 Valuation of a synthetic CDO..............................................................583
25.11 Alternatives to the standard market model.............................................590
Summary..........................................................................................592
Further reading..................................................................................592
Practice questions...............................................................................593
Further questions...............................................................................594
Chapter26. Exotic options.............................................................................................596
26.1 Packages...........................................................................................596
26.2 Perpetual American call and put options...............................................597
26.3 Nonstandard American options............................................................598
26.4 Gap options......................................................................................599
26.5 Forward start options.........................................................................600
26.6 Cliquet options..................................................................................600
26.7 Compound options.............................................................................600
26.8 Chooser options.................................................................................601
26.9 Barrier options..................................................................................602
26.10 Binary options...................................................................................604
26.11 Lookback options..............................................................................605
26.12 Shout options....................................................................................607
26.13 Asian options....................................................................................608
26.14 Options to exchange one asset for another.............................................609
26.15 Options involving sever alassets............................................................610
26.16 Volatility and variance swaps...............................................................611
26.17 Static options replication.....................................................................614
Summary..........................................................................................616
Further reading..................................................................................617
Practice questions...............................................................................617
Further questions...............................................................................619
Chapter27. More on models and numerical procedures........................................................622
27.1 Alternatives to Black-Scholes-Merton..................................................623
27.2 Stochastic volatility models..................................................................628
27.3 The IVF model..................................................................................630
27.4 Convertible bonds..............................................................................632
27.5 Path-dependent derivatives...................................................................634
27.6 Barrier options..................................................................................637
27.7 Options on two correlated assets..........................................................640
27.8 Monte Carlo simulation and American options......................................642
Summary..........................................................................................646
Further reading..................................................................................647
Practice questions...............................................................................648
Further questions...............................................................................650
Chapter28. Martingales and measures..............................................................................652
28.1 The market price of risk......................................................................653
28.2 Several state variables..........................................................................656
28.3 Martingales........................................................................................657
28.4 Alternative choices for the numeraire.....................................................658
28.5 Extension to several factors..................................................................661
28.6 Black抯 model revisited........................................................................662
28.7 Option to exchange one asset for another...............................................663
28.8 Change of numeraire...........................................................................664
Summary...........................................................................................666
Further reading..................................................................................667
Practice questions................................................................................667
Further questions................................................................................668
Chapter29. Interest rate derivatives: The standard market models..........................................670
29.1 Bond options.....................................................................................670
29.2 Interest rate caps and oors..................................................................675
29.3 European swa poptions........................................................................681
29.4 Hedging interest rate derivatives............................................................684
Summary...........................................................................................685
Further reading..................................................................................686
Practice questions................................................................................686
Further questions................................................................................688
Chapter30. Convexity, timing, and quanto adjustments........................................................689
30.1 Convexity adjustments.........................................................................689
30.2 Timing adjustments.............................................................................693
30.3 Quantos............................................................................................695
Summary...........................................................................................698
Further reading..................................................................................698
Practice questions................................................................................698
Further questions................................................................................700
Appendix: Proof of the convexity adjustment formula..............................701
Chapter31.Equilibrium models of the short rate.................................................................702
31.1 Background.......................................................................................702
31.2 One-factor models...............................................................................704
31.3 Real-world vs. risk-neutral processes......................................................709
31.4 Estimating parameters.........................................................................710
31.5 More sophisticated models...................................................................711
Summary...........................................................................................712
Further reading..................................................................................712
Practice questions................................................................................712
Further questions................................................................................713
Chapter32. No-arbitrage models of the short rate...............................................................715
32.1 Extensions of equilibrium models..........................................................715
32.2 Options on bonds...............................................................................719
32.3 Volatility structures.............................................................................720
32.4 Interest rate trees................................................................................721
32.5 A general tree-building procedure..........................................................723
32.6 Calibration.........................................................................................732
32.7 Hedging usinga one-factor model.........................................................734
Summary...........................................................................................735
Further reading..................................................................................735
Practice questions...............................................................................735
Further questions...............................................................................736
Chapter33.HJM, LMM, and multiple zero curves............................................................738
33.1 The Heath, Jarrow, and Morton model.................................................738
33.2 The LIBOR market model..................................................................741
33.3 Handling multiple zero curves..............................................................751
33.4 Agency mortgage-backed securities.......................................................752
Summary..........................................................................................754
Further reading..................................................................................755
Practice questions...............................................................................755
Further questions...............................................................................756
Chapter34. Swaps Revisited...........................................................................................757
34.1 Variations on the vanilla deal..............................................................757
34.2 Compounding swaps...........................................................................759
34.3 Currency swaps..................................................................................760
34.4 More complexs waps..........................................................................761
34.5 Equity swaps.....................................................................................764
34.6 Swaps with embedded options..............................................................765
34.7 Other swaps......................................................................................768
Summary..........................................................................................769
Further reading..................................................................................770
Practice questions...............................................................................770
Further questions...............................................................................770
Chapter35. Energy and commodity derivatives......................................................772
35.1 Agricultural commodities....................................................................772
35.2 Metals..............................................................................................773
35.3 Energy products.................................................................................774
35.4 Modeling commodity prices.................................................................776
35.5 Weather derivatives.............................................................................782
35.6 Insurance derivatives...........................................................................783
35.7 Pricing weather and insurance derivatives...............................................784
35.8 How an energy producer can hedge risks...............................................785
Summary..........................................................................................786
Further reading..................................................................................786
Practice questions...............................................................................787
Further question................................................................................788
Chapter36. Real options.........................................................................789
36.1 Capital investment appraisal................................................................789
36.2 Extension of the risk-neutral valuation framework..................................790
36.3 Estimating the market price of risk.......................................................792
36.4 Application to the valuation of a business.............................................793
36.5 Evaluating options in an investment opportunity....................................793
Summary..........................................................................................800
Further reading..................................................................................800
Practice questions...............................................................................801
Further questions...............................................................................801
Chapter37. Derivatives mishaps and what we can learn from them........................................803
37.1 Lessons for all users of derivatives........................................................803
37.2 Lessons for nancial institutions...........................................................807
37.3 Lessons for nonnancial corporations...................................................812
Summary...........................................................................................814
Further reading..................................................................................814
Appendix A. DerivaGem software......................................................................815
Appendix B. Major exchanges trading futures and options....................................................820
Appendix C. Table for N(x) when x≤0............................................................821
Appendix D. Table for N(x) when x≥0........................................................822
