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【经典推荐】金融风险和衍生证券定价理论——从统计物理到风险管理

风控博士沙龙2019-06-28 23:35:59



《金融风险和衍生证券定价理论——从统计物理到风险管理》(英文名“Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management”)是用物理学的分析方法处理金融风险的书,它涉及到混沌、分形、厚尾分布等等一些金融风险领域的理论和方法。书中提出了不少问题,给出了一些解决的办法和结论,这是和经济学家们写法完全不同(与数学家、计量经济学家也不同)的一本书。书中分析了风险的来源是中心极限定理中收敛的不一致性,重点介绍了金融风险的控制和管理,作者提供了很多定价、风险评估以及组合管理的算法和理论。


本书的最新版是第二版,于2003年12月由剑桥大学出版社(Cambridge University Press)出版,本书第一版中文版于2002年8月由经济科学出版社出版。


作者简介


Jean-Philippe Bouchaud: co-founded the company Science & Finance, which merged with Capital Fund Management (CFM) in 2000, where he now supervises the research team with Marc Potters. He teaches statistical mechanics and finance in various Grandes Écoles, and has worked at CRNS and CEA-Saclay. He was awarded the CRNS Silver Medal in 1996.

 

Marc Potters: Head of Research at CFM since 1998, where he supervises thirty physics PhD's. He has published numerous articles in the new field of statistical finance, in particular on Random Matrix Theory applied to portfolio management. He works on various concrete applications of financial forecasting, option pricing and risk control.


目录


1 Probability theory: basic notions

1.1 Introduction

1.2 Probability distributions

1.3 Typical values and deviations

1.4 Moments and characteristic function

1.5 Divergence of moments-asymptotic behaviour

1.6 Gaussian distribution

1.7 Log-normal distribution

1.8 Levy distributions and Paretian tails

1.9 Other distributions (*)

1.10 Summary

 

2 Maximum and addition of random variables

2.1 Maximum of random variables

2.2 Sums of random variables

2.2.1 Convolutions

2.2.2 Additivity of cumulants and of tail amplitudes

2.2.3 Stable distributions and self-similarity

2.3 Central limit theorem

2.3.1 Convergence to a Gaussian

2.3.2 Convergence to a Levy distribution

2.3.3 Large deviations

2.3.4 Steepest descent method and Cram~~r function (*)

2.3.5 The CLT at work on simple cases

2.3.6 Truncated L6vy distributions

2.3.7 Conclusion: survival and vanishing of tails

2.4 From sum to max: progressive dominance of extremes (*)

2.5 Linear correlations and fractional Brownian motion

2.6 Summary

 

3 Continuous time limit, Ito calculus and path integrals

3. I Divisibility and the continuous time limit

3.1.1 Divisibility

3.1.2 Infinite divisibility

3.1.3 Poisson jump processes

3.2 Functions of the Brownian motion and Ito calculus

3.2.1 Ito's lemma

3.2.2 Novikov's formula

3.2.3 Stratonovich's prescription

3.3 Other techniques

3.3.1 Path integrals

3.3.2 Girsanov's formula and the Martin-Siggia-Rose trick

3.4 Summary

 

4 Analysis of empirical data

4.1 Estimating probability distributions

4.1.1 Cumulative distribution and densities - rank histogram

4.1.2 Kolmogorov-Smirnov test

4.1.3 Maximum likelihood

4.1.4 Relative likelihood

4.1.5 A general caveat

4.2 Empirical moments: estimation and error

4.2.1 Empirical mean

4.2.2 Empirical variance and MAD

4.2.3 Empirical kurtosis

4.2.4 Error on the volatility

4.3 Correlograms and variograms

4.3.1 Variogram

4.3.2 Correlogram

4.3.3 Hurst exponent

4.3.4 Correlations across different time zones

4.4 Data with heterogeneous volatilities

4.5 Summary

 

5 Financial products and financial markets

5.1 Introduction

5.2 Financial products

5.2.1 Cash (Interbank market)

5.2.2 Stocks

5.2.3 Stock indices

5.2.4 Bonds

5.2.5 Commodities

5.2.6 Derivatives

5.3 Financial markets

5.3.1 Market participants

5.3.2 Market mechanisms

5.3.3 Discreteness

5.3.4 The order book

5.3.5 The bid-ask spread

5.3.6 Transaction costs

5.3.7 Time zones, overnight, seasonalities

5.4 Summary

 

6 Statistics of real prices: basic results

6.1 Aim of the chapter

6.2 Second-order statistics

6.2.1 Price increments vs. returns

6.2.2 Autocorrelation and power spectrum

6.3 Distribution of returns over different time scales

6.3.1 Presentation of the data

6.3.2 The distribution of returns

6.3.3 Convolutions

6.4 Tails, what tails

6.5 Extreme markets

6.6 Discussion

6.7 Summary

 

7 Non-linear correlations and volatility fluctuations

7.1 Non-linear correlations and dependence

7.1.1 Non identical variables

7.1.2 A stochastic volatility model

7.1.3 GARCH(I,I)

7.1.4 Anomalous kurtosis

7.1.5 The case of infinite kurtosis

7.2 Non-linear correlations in financial markets: empirical results

7.2.1 Anomalous decay of the cumulants

7.2.2 Volatility correlations and variogram

7.3 Models and mechanisms

7.3.1 Multifractality and multifractal models (*)

7.3.2 The microstructure of volatility

7.4 Summary

 

8 Skewness and price-volatility correlations

8.1 Theoretical considerations

8.1.1 Anomalous skewness of sums of random variables

8.1.2 Absolute vs. relative price changes

8.1.3 The additive-multiplicative crossover and the q-transformation

8.2 A retarded model

8.2.1 Definition and basic properties

8.2.2 Skewness in the retarded model

8.3 Price-volatility correlations: empirical evidence

8.3.1 Leverage effect for stocks and the retarded model

8.3.2 Leverage effect for indices

8.3.3 Return-volume correlations

8.4 The Heston model: a model with volatility fluctuations and skew

8.5 Summary

 

9 Cross-correlations

9.1 Correlation matrices and principal component analysis

9.1.1 Introduction

9.1.2 Gaussian correlated variables

9.1.3 Empirical correlation matrices

9.2 Non-Gaussian correlated variables

9.2.1 Sums of non Gaussian variables

9.2.2 Non-linear transformation of correlated Gaussian variables

9.2.3 Copulas

9.2.4 Comparison of the two models

9.2.5 Multivariate Student distributions

9.2.6 Multivariate L~~vy variables (*)

9.2.7 Weakly non Gaussian correlated variables (*)

9.3 Factors and clusters

9.3.1 One factor models

9.3.2 Multi-factor models

9.3.3 Partition around medoids

9.3.4 Eigenvector clustering

9.3.5 Maximum spanning tree

9.4 Summary

9.5 Appendix A: central limit theorem for random matrices

9.6 Appendix B: density of eigenvalues for random correlation matrices

 

10 Risk measures

10.1 Risk measurement and diversification

10.2 Risk and volatility

10.3 Risk of loss, 'value at

10.4 Temporal aspects: drawdown and cumulated loss

10.5 Diversification and utility-satisfaction thresholds

10.6 Summary

 

11 Extreme correlations and variety

11.1 Extreme event correlations .

11.1.1 Correlations conditioned on large market moves

11.1.2 Real data and surrogate data

11.1.3 Conditioning on large individual stock returns: exceedance correlations

11.1.4 Tail dependence

11.1.5 Tail covariance (*)

11.2 Variety and conditional statistics of the residuals

11.2.1 The variety

11.2.2 The variety in the one-factor model

11.2.3 Conditional variety of the residuals

11.2.4 Conditional skewness of the residuals

11.3 Summary

11.4 Appendix C: some useful results on power-law variables

 

12 Optimal portfolios

12.1 Portfolios of uncorrelated assets

12.1.1 Uncorrelated Gaussian assets

12.1.2 Uncorrelated 'power-law' assets

12.1.3 Exponential' assets

12.1.4 General case: optimal portfolio and VaR (*)

12.2 Portfolios of correlated assets

12.2.1 Correlated Gaussian fluctuations

12.2.2 Optimal portfolios with non-linear constraints (*)

12.2.3 'Power-law' fluctuations - linear model (*)

12.2.4 'Power-law' fluctuations - Student model (*)

12.3 Optimized trading

12.4 Value-at-risk- general non-linear portfolios (*)

12.4.1 Outline of the method: identifying worst cases

12.4.2 Numerical test of the method

12.5 Summary

 

13 Futures and options: fundamental concepts

13.1 Introduction

13.1.1 Aim of the chapter

13.1.2 Strategies in uncertain conditions

13.1.3 Trading strategies and efficient markets

13.2 Futures and forwards

13.2.1 Setting the stage

13.2.2 Global financial balance

13.2.3 Riskless hedge

13.2.4 Conclusion: global balance and arbitrage

13.3 Options: definition and valuation

13.3.1 Setting the stage

13.3.2 Orders of magnitude

13.3.3 Quantitative

 

14 Options: hedging and residual risk

14.1 Introduction

14.2 Optimal hedging strategies

14.2.1 A simple case: static hedging

14.2.2 The general case and 'A' hedging

14.2.3 Global hedging vs. instantaneous hedging

14.3 Residual risk

14.3.1 The Black-Scholes miracle

14.3.2 The 'stop-loss' strategy does not work

14.3.3 Instantaneous residual risk and kurtosis risk

14.3.4 Stochastic volatility models

14.4 Hedging errors. A variational point of view

14.5 Other measures of risk-hedging and VaR (*)

14.6 Conclusion of the chapter

14.7 Summary

14.8 Appendix D

 

15 Options: the role of drift and correlations

15.1 Influence of drift on optimally hedged option

15.1.1 A perturbative expansion

15.1.2 'Risk neutral' probability and martingales

15.2 Drift risk and delta-hedged options

15.2.1 Hedging the drift risk

15.2.2 The price of delta-hedged options

15.2.3 A general option pricing formula

15.3 Pricing and hedging in the presence of temporal correlations (*)

15.3.1 A general model of correlations

15.3.2 Derivative pricing with small correlations

15.3.3 The case of delta-hedging

15.4 Conclusion

15.4.1 Is the price of an option unique

15.4.2 Should one always optimally hedge

15.5 Summary

15.6 Appendix E

 

16 Options: the Black and Scholes model

16.1 Ito calculus and the Black-Scholes equation

16.1.1 The Gaussian Bachelier model

16.1.2 Solution and Martingale

16.1.3 Time value and the cost of hedging

16.1.4 The Log-normal Black-Scholes model

16.1.5 General pricing and hedging in a Brownian world

16.1.6 The Greeks

16.2 Drift and hedge in the Gaussian model (*)

16.2.1 Constant drift

16.2.2 Price dependent drift and the Omstein-Uhlenbeck paradox

16.3 The binomial model

16.4 Summary

 

17 Options: some more specific

17.1.3 Discrete dividends

17.1.4 Transaction costs

17.2 Other types of options

17.2.1 'Put-call' parity

17.2.2 'Digital' options

17.2.3 'Asian' options

17.2.4 'American' options

17.2.5 'Barrier' options (*)

17.2.6 Other types of options

17.3 The 'Greeks' and risk control

17.4 Risk diversification (*)

17.5 Summary

 

18 Options: minimum variance Monte-Carlo

18.1 Plain Monte-Carlo

18.1.1 Motivation and basic principle

18.1.2 Pricing the forward exactly

18.1.3 Calculating the Greeks

18.1.4 Drawbacks of the method

18.2 An 'hedged' Monte-Carlo method

18.2.1 Basic principle of the method

18.2.2 A linear parameterization of the price and hedge

18.2.3 The Black-Scholes limit

18.3 Non Gaussian models and purely historical option pricing

18.4 Discussion and extensions. Calibration

18.5 Summary

18.6 Appendix F: generating some random variables

 

19 The yield curve

19.1 Introduction

19.2 The bond market

19.3 Hedging bonds with other bonds

19.3.1 The general problem

19.3.2 The continuous time Ganssian limit

19.4 The equation for bond pricing

19.4.1 A general solution

19.4.2 The Vasicek model

19.4.3 Forward rates

19.4.4 More general models

19.5 Empirical study of the forward rate curve

19.5.1 Data and notations

19.5.2 Quantities of interest and data analysis

19.6 Theoretical considerations (*)

19.6.1 Comparison with the Vasicek model

19.6.2 Market price of risk

19.6.3 Risk-premium and the law

19.7 Summary

19.8 Appendix G: optimal portfolio of bonds

 

20 Simple mechanisms for anomalous price statistics

20.1 Introduction

20.2 Simple models for herding and mimicry

20.2.1 Herding and percolation

20.2.2 Avalanches of opinion changes

20.3 Models of feedback effects on price fluctuations

20.3.1 Risk-aversion induced crashes

20.3.2 A simple model with volatility correlations and tails

20.3.3 Mechanisms for long ranged volatility correlations

20.4 The Minority Game

20.5 Summary

Index of most important symbols

Index



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