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Study Of Math Health Studyofmath Oskar Study Of Math

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如果有兴趣，你当然可以把Neftci(2000)从头到尾读下来，对金融数学要求的随机微积分了解个通透。这本书会从导数的定义开始，一直讲到我们需要的Itō积分、鞅还有PDE，它是Wilmott(2006)还有Hull(2006)都推荐的书（Wilmott看着就是追随这本）。当然，Hull的相关章节（加上附录）也是我们初步了解随机微积分的极好途径，其他的书大都藏头藏尾，遮遮掩掩。有本中文书，台湾陈松男(2002)，不回避大多数学问题，读着也是痛快淋漓，而且提供了大多数教科书不曾见到的数学细节。以下这个读书笔记，参照的就是Hull和陈松男（下面当然不好显示数学符号，你可以在我的 Page找到下文详细的pdf版本，一个叫FinancialStochasticCalculus.pdf    的文件）：

  1. 马尔科夫过程(Markov Stochastic Process)
  2. 维纳过程(Wiener Process)
  3. Delta(z)的概率分布性质
  4. 把时段的长度放大至T
  5. 一般化的维纳过程
  6. 伊藤过程(Itō Process)
  7. 伊藤引理(Itō’s Lemma)
  8. 伊藤引理(Itō’s Lemma)的扩展
  9. 股票价格的变动过程
  10. 伊藤引理应用于股价的变动过程

参考文献

  1. Paul Wilmott. Paul Wilmott on Quantitative Finance (Volume One, 2nd Ed.).John Wiley &Sons, 2006
  2. Salih N. Neftci. An Introduction to the Mathematics of Financial Derivatives (2nd Ed., 2000). 武汉大学出版社影印版，2007
  3. John C. Hull. Options, Futures and Other Derivatives (6th Ed.). Prentice Hall, 2006
  4. 陈松男《金融工程学——金融商品创新选择权理论》，复旦大学出版社，2002

5 Comments

Paul Wilmott’s Books on Quantitative Finance

December 5th, 2007 — 金融计算

Paul Wilmott在数量金融(Quantitative Finance)方面的书，跟Fabozzi（发包子）在固定收益(Fixed Income)方面的书一样有名，一样充满重复，不过捡来的声誉要高得多。现在有朋友问，他哪些书值得买（或者复印、打印），其实这个问题Paul写书之前——我看——就给出了答案。他最有名的书，Paul Wilmott on Quantitative Finance，以前是两卷本（2000，1064页），现在是三卷（2006，1500页），手头备一份就可以了。如果还嫌贵，Paul还准备了一册Paul Wilmott Introduces Quantitative Finance（2007，722页），是上面三卷本的精简版。

是已经够了。不过在国内，还偶尔能看到Paul的另一本Derivatives: the Theory and Practice of Financial Engineering（1998，768页），或者一册更薄的，The Mathematics of Financial Derivatives: A Student Introduction（1995，330页），这本小书又是他的Option Pricing: mathematical Methods and Computation（1994，457页）的缩写。

这些书章节惊人的重复，大概看看下面的几个目录就可以决定取舍了：

Paul Wilmott on Quantitative Finance三卷本（2006，1500页）

第一卷

1. Products and Markets
2. Derivatives
3. The Random Behavior of Assets
4. Elementary Stochastic Calculus
5. The Black-Scholes Model
6. Partial Differential Equations
7. The Black-Scholes Formulae and the ‘Greeks’
8. Simple Generalizations of the Black-Scholes World
9. Early Exercise and American Options
10. Probability Density Functions and First Exit Times
11. Multi-asset Options
12. How to Delta Hedge
13. Fixed-income Products and Analysis: Yield, Duration and Convexity
14. Swaps
15. The Binomial Model
16. How Accurate is the Normal Approximation?
17. Investment Lessons from Blackjack and Gambling
18. Portfolio Management
19. Value at Risk
20. Forecasting the Markets?
21. A Trading Game

第二卷

22. An Introduction to Exotic and Path-dependent Options
23. Barrier Options
24. Strongly Path-dependent Options
25. Asian Options
26. Lookback Options
27. Derivatives and Stochastic Control
28. Miscellaneous Exotics
29. Equity and FX Term Sheets
30. One-factor Interest Rate Modeling
31. Yield Curve Fitting
32. Interest Rate Derivatives
33. Convertible Bonds
34. Mortgage-backed Securities
35. Multi-factor Interest Rate Modeling
36. Empirical Behavior of the Spot Interest Rate
37. The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models
38. Fixed Income Term Sheets
39. Value of the Firm and the Risk of Default
40. Credit Risk
41. Credit Derivatives
42. RiskMetrics and CreditMetrics
43. CrashMetrics
44. Derivatives **** Ups

第三卷

45. Financial Modeling
46. Defects in the Black-Scholes Model
47. Discrete Hedging
48. Transaction Costs
49. Overview of Volatility Modeling
50. Volatility Smiles and Surfaces
51. Stochastic Volatility
52. Uncertain Parameters
53. Empirical Analysis of Volatility
54. Stochastic Volatility and Mean-variance Analysis
55. Asymptotic Analysis of Volatility
56. Volatility Case Study: The Cliquet Option
57. Jump Diffusion
58. Crash Modeling
59. Speculating with Options
60. Static Hedging
61. The Feedback Effect of Hedging in Illiquid Markets
62. Utility Theory
63. More About American Options and Related Matters
64. Advanced Dividend Modeling
65. Serial Autocorrelation in Returns
66. Asset Allocation in Continuous Time
67. Asset Allocation Under Threat Of A Crash
68. Interest-rate Modeling Without Probabilities
69. Pricing and Optimal Hedging of Derivatives, the Non-probabilistic Model Cont’d
70. Extensions to the Non-probabilistic Interest-rate Model
71. Modeling Inflation
72. Energy Derivatives
73. Real Options
74. Life Settlements and Viaticals
75. Bonus Time
76. Overview of Numerical Methods
77. Finite-difference Methods for One-factor Models
78. Further Finite-difference Methods for One-factor Models
79. Finite-difference Methods for Two-factor Models
80. Monte Carlo Simulation and Related Methods
81. Numerical Integration and Simulation Methods
82. Finite-difference Programs
83. Monte Carlo Programs
A. All the Math You Need… and No More (An Executive Summary)

Paul Wilmott Introduces Quantitative Finance

1 Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures

2 Derivatives

3 The Binomial Model

4 The Random Behavior of Assets

5 Elementary Stochastic Calculus 

6 The Black-Scholes Model

7 Partial Differential Equations

8 The Black-Scholes Formula and the ‘Greeks’

9 Overview of Volatility Modeling

10 How to Delta Hedge

11 An Introduction to Exotic and Path-dependent Options

12 Multi-asset Options

13 Barrier Options

14 Fixed-income Products and Analysis: Yield, Duration and Convexity

15 Swaps

16 One-factor Interest Rate Modeling

17 Yield Curve Fitting

18 Interest Rate Derivatives

19 The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models

20 Investment Lessons from Blackjack and Gambling

21 Portfolio Management

22 Value at Risk

23 Credit Risk

24 RiskMetrics and CreditMetrics

25 CrashMetrics

26 Derivatives **** Ups

27 Overview of Numerical Methods

28 Finite-difference Methods for One-factor Models

29 Monte Carlo Simulation

30 Numerical Integration

A All the Math You Need. . . and No More (An Executive Summary)

B Forecasting the Markets? A Small Digression

C A Trading Game

D Contents of CD accompanying Paul Wilmott Introduces Quantitative Finance, second edition

E What you get if (when) you upgrade to PWOQF2

Bibliography

Index

 

The Mathematics of Financial Derivatives: A Student Introduction

PART I: Basic Option Theory
1. An Introduction to Options and Markets
2. Asset Price Random Walks
3. The Black-Scholes Model
4. Partial Differential Equations
5. The Black-Scholes Formulae
6. Variations on the Black-Scholes Model
7. American Options
PART II: Numerical Methods
8. Finite-Difference Methods
9. Methods for American Options
10. Binomial Methods
PART III: Further Option Theory
11. Exotic and Path-Dependent Options
12. Barrier Options
13. A Unifying Framework for Path-Dependent Options
14. Asian Options
15. Lookback Options
16. Options with Transaction Costs
PART IV: Interest Rate Derivative Products
17. Interest rate Derivatives
18. Convertible Bonds
Hints to Selected Exercises
Bibliography
Index

2 Comments

提升指数、提升表和提升图

September 19th, 2007 — 金融计算

——————–

这篇去年在我的生活博客出现过，题目叫《贴一篇读书报告：Lift,Lift Table, and Lift Chart》。不想年代久远，里面的一个表格不知道怎么没有了，现挪到自己这个（所谓）技术博客，除了补全，也算是回到正确的地方了。从本机文档中直接COPY过来，删掉一些废话。

——————–

Lift, Lift Table, and Lift Chart

提升指数、提升表和提升图（草稿）

胡江堂，北京大学软件与微电子学院

2006-11-5

 

1. 什么是Lift？

I) Lift（提升指数）是评估一个预测模型是否有效的一个度量；这个比值由运用和不运用这个模型所得来的结果计算而来。

II) 一个简单的数字例子：

i. 比如说你要向选定的1000人邮寄调查问卷。以往的经验告诉你大概20%的人会把填好的问卷寄回给你，即1000人中有200人会对你的问卷作出回应（response），用统计学的术语，我们说baseline response rate是20%；

ii. 如果你现在就邮寄问卷，1000份你期望能收回200份，这可能达不到一次问卷调查所要求的回收率，比如说工作手册规定邮寄问卷回收率要在25%以上；

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