Summarizing market data developments, some inspired by statistical physics, this book explains how to better predict the actual behavior of financial markets with respect to asset allocation, derivative pricing and hedging, and risk control. Risk control and derivative pricing are major concerns to financial institutions. The need for adequate statistical tools to measure and anticipate amplitude of potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on assumptions leading to systematic (sometimes dramatic) underestimation of risks.
- Now expanded to include stochastic processes, data analysis, estimate techniques, path integrals, Ito calculus and much more
- New chapters cast a fresh look at derivative pricing, financial products and markets which is completely different from anything else available in the literature
- Contains a mixture of cutting edge results and basic knowledge to make for the most complete and up-to-date text on the subject
Author(s): Jean-Philippe Bouchaud, Marc Potters
Edition: 2
Publisher: Cambridge University Press
Year: 2004
Language: English
Pages: 401
Tags: derivatives,finance,risk,pricing
Contents
Foreword
Preface
Scope of the book
Style and organization of the book
Comparison with the previous editions
Acknowledgements †
Further reading
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 L´evy distributions and Paretian tails
1.9 Other distributions ( ∗ )
1.10 Summary
2 - Maximum and addition of random variables
2.1 Maximum of random variables – statistics of extremes
2.2 Sums of random variables
2.3 Central limit theorem
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
3.1 Divisibility and the continuous time limit
3.2 Functions of the Brownian motion and Ito calculus
3.3 Other techniques
3.4 Summary
4 - Analysis of empirical data
4.1 Estimating probability distributions
4.2 Empirical moments: estimation and error
4.3 Correlograms and variograms
4.4 Data with heterogeneous volatilities
4.5 Summary
5 - Financial products and financial markets
5.1 Introduction
5.2 Financial products
5.3 Financial markets
5.4 Summary
6 - Statistics of real prices: basic results
6.1 Aim of the chapter
6.2 Second-order statistics
6.3 Distribution of returns over different time scales
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
7.2 Non-linear correlations in financial markets: empirical results
7.3 Models and mechanisms
7.4 Summary
8 - Skewness and price-volatility correlations
8.1 Theoretical considerations
8.2 A retarded model
8.3 Price-volatility correlations: empirical evidence
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
9.2 Non-Gaussian correlated variables
9.3 Factors and clusters
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-risk’ (VaR) and expected shortfall
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
11.2 Variety and conditional statistics 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
12.2 Portfolios of correlated assets
12.3 Optimized trading
12.4 Value-at-risk for general non-linear portfolios ( ∗ )
12.5 Summary
13 - Futures and options: fundamental concepts
13.1 Introduction
13.2 Futures and forwards
13.3 Options: definition and valuation
13.4 Summary
14 - Options: hedging and residual risk
14.1 Introduction
14.2 Optimal hedging strategies
14.3 Residual risk
14.4 Hedging errors. A variational point of view
14.5 Other measures of risk – hedging and VaR ( ∗ )
14.6 Conclusion of the chapter: the pitfalls of zero-risk
14.7 Summary
14.8 Appendix D: computation of the conditional mean
15 - Options: The role of drift and correlations
15.1 The influence of drift on an optimally hedged option
15.2 Drift risk and delta-hedged options
15.3 Pricing and hedging in the presence of temporal correlations ( ∗ )
15.4 Conclusion
15.5 Summary
15.6 Appendix E: optimal strategy in the presence of a bias
16 - Options: the Black and Scholes model
16.1 Ito calculus and the Black-Scholes equation
16.2 Drift and hedge in the Gaussian model ( ∗ )
16.3 The binomial model
16.4 Summary
17 - Options: some more specific problems
17.1 Other elements of the balance sheet
17.2 Other types of options: ‘puts’ and ‘exotic 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
18.2 An ‘hedged’ Monte-Carlo method
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
19.4 The equation for bond pricing
19.5 Empirical study of the forward rate curve
19.6 Theoretical considerations ( ∗ )
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
20.3 Models of feedback effects on price fluctuations
20.4 The Minority Game
20.5 Summary
Index of most important symbols
Index
