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## Book Description

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising recent theoretical developments in the field, this second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

1. Cover
2. Title
4. Contents
5. Foreword
6. Preface
7. 1 Probability theory: basic notions
8. 2 Maximum and addition of random variables
1. 2.1 Maximum of random variables
2. 2.2 Sums of random variables
3. 2.3 Central limit theorem
4. 2.4 From sum to max: progressive dominance of extremes (*)
5. 2.5 Linear correlations and fractional Brownian motion
6. 2.6 Summary
9. 3 Continuous time limit, Ito calculus and path integrals
1. 3.1 Divisibility and the continuous time limit
2. 3.2 Functions of the Brownian motion and Ito calculus
3. 3.3 Other techniques
4. 3.4 Summary
10. 4 Analysis of empirical data
1. 4.1 Estimating probability distributions
2. 4.2 Empirical moments: estimation and error
3. 4.3 Correlograms and variograms
4. 4.4 Data with heterogeneous volatilities
5. 4.5 Summary
11. 5 Financial products and financial markets
1. 5.1 Introduction
2. 5.2 Financial products
3. 5.3 Financial markets
4. 5.4 Summary
12. 6 Statistics of real prices: basic results
1. 6.1 Aim of the chapter
2. 6.2 Second-order statistics
3. 6.3 Distribution of returns over different time scales
4. 6.4 Tails, what tails?
5. 6.5 Extreme markets
6. 6.6 Discussion
7. 6.7 Summary
13. 7 Non-linear correlations and volatility fluctuations
1. 7.1 Non-linear correlations and dependence
2. 7.2 Non-linear correlations in financial markets: empirical results
3. 7.3 Models and mechanisms
4. 7.4 Summary
14. 8 Skewness and price-volatility correlations
1. 8.1 Theoretical considerations
2. 8.2 A retarded model
3. 8.3 Price-volatility correlations: empirical evidence
4. 8.4 The Heston model: a model with volatility fluctuations and skew
5. 8.5 Summary
15. 9 Cross-correlations
1. 9.1 Correlation matrices and principal component analysis
2. 9.2 Non-Gaussian correlated variables
3. 9.3 Factors and clusters
4. 9.4 Summary
5. 9.5 Appendix A: central limit theorem for random matrices
6. 9.6 Appendix B: density of eigenvalues for random correlation matrices
16. 10 Risk measures
1. 10.1 Risk measurement and diversification
2. 10.2 Risk and volatility
3. 10.3 Risk of loss, ‘value at risk’ (VaR) and expected shortfall
4. 10.4 Temporal aspects: drawdown and cumulated loss
5. 10.5 Diversification and utility – satisfaction thresholds
6. 10.6 Summary
17. 11 Extreme correlations and variety
1. 11.1 Extreme event correlations
2. 11.2 Variety and conditional statistics of the residuals
3. 11.3 Summary
4. 11.4 Appendix C: some useful results on power-law variables
18. 12 Optimal portfolios
1. 12.1 Portfolios of uncorrelated assets
2. 12.2 Portfolios of correlated assets
4. 12.4 Value-at-risk – general non-linear portfolios (*)
5. 12.5 Summary
19. 13 Futures and options: fundamental concepts
1. 13.1 Introduction
2. 13.2 Futures and forwards
3. 13.3 Options: definition and valuation
4. 13.4 Summary
20. 14 Options: hedging and residual risk
1. 14.1 Introduction
2. 14.2 Optimal hedging strategies
3. 14.3 Residual risk
4. 14.4 Hedging errors. A variational point of view
5. 14.5 Other measures of risk – hedging and VaR (*)
6. 14.6 Conclusion of the chapter
7. 14.7 Summary
8. 14.8 Appendix D
21. 15 Options: the role of drift and correlations
1. 15.1 Influence of drift on optimally hedged option
2. 15.2 Drift risk and delta-hedged options
3. 15.3 Pricing and hedging in the presence of temporal correlations (*)
4. 15.4 Conclusion
5. 15.5 Summary
6. 15.6 Appendix E
22. 16 Options: the Black and Scholes model
1. 16.1 Ito calculus and the Black-Scholes equation
2. 16.2 Drift and hedge in the Gaussian model (*)
3. 16.3 The binomial model
4. 16.4 Summary
23. 17 Options: some more specific problems
1. 17.1 Other elements of the balance sheet
2. 17.2 Other types of options
3. 17.3 The ‘Greeks’ and risk control
4. 17.4 Risk diversification (*)
5. 17.5 Summary
24. 18 Options: minimum variance Monte–Carlo
1. 18.1 Plain Monte-Carlo
2. 18.2 An ‘hedged’ Monte-Carlo method
3. 18.3 Non Gaussian models and purely historical option pricing
4. 18.4 Discussion and extensions. Calibration
5. 18.5 Summary
6. 18.6 Appendix F: generating some random variables
25. 19 The yield curve
1. 19.1 Introduction
2. 19.2 The bond market
3. 19.3 Hedging bonds with other bonds
4. 19.4 The equation for bond pricing
5. 19.5 Empirical study of the forward rate curve
6. 19.6 Theoretical considerations (*)
7. 19.7 Summary
8. 19.8 Appendix G: optimal portfolio of bonds
26. 20 Simple mechanisms for anomalous price statistics
1. 20.1 Introduction
2. 20.2 Simple models for herding and mimicry
3. 20.3 Models of feedback effects on price fluctuations
4. 20.4 The Minority Game
5. 20.5 Summary
27. Index of most important symbols
28. Index