Theory of financial risks : from statistical physics to risk management
Summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. Of interest to physicists, quantitative analysts in financial institutions, risk managers and graduat...
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| Format: | eBook Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2000
Cambridge Univ. Press |
| Edition: | 1 |
| Subjects: | |
| ISBN: | 9780521782326, 0521782325 |
| Online Access: | Get full text |
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| Abstract | Summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. Of interest to physicists, quantitative analysts in financial institutions, risk managers and graduate students in mathematical finance. |
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| AbstractList | Summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. Of interest to physicists, quantitative analysts in financial institutions, risk managers and graduate students in mathematical finance. This book summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. The possibility of accessing and processing huge quantities of data on financial markets opens the path to new methodologies where systematic comparison between theories and real data not only becomes possible, but mandatory. This book takes a physicist's point of view to financial risk by comparing theory with experiment. Starting with important results in probability theory, the authors discuss the statistical analysis of real data, the empirical determination of statistical laws, the definition of risk, the theory of optimal portfolio, and the problem of derivatives (forward contracts, options). This book will be of interest to physicists interested in finance, quantitative analysts in financial institutions, risk managers and graduate students in mathematical finance. |
| Author | Potters, Marc Bouchaud, Jean-Philippe |
| Author_xml | – sequence: 1 fullname: Bouchaud, Jean-Philippe – sequence: 2 fullname: Potters, Marc |
| BackLink | https://cir.nii.ac.jp/crid/1130000796523445632$$DView record in CiNii http://www.econis.eu/PPNSET?PPN=320665151$$DView this record in ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften |
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| Discipline | Business |
| EISBN | 9780511151255 051115125X 0511030983 9780511030987 |
| Edition | 1 1st publ |
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| ISBN | 9780521782326 0521782325 |
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| Notes | Includes bibliographical references and indexes |
| OCLC | 70738663 |
| PQID | EBC143920 |
| PageCount | 234 |
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| PublicationCentury | 2000 |
| PublicationDate | 2000 2005-01-28 |
| PublicationDateYYYYMMDD | 2000-01-01 2005-01-28 |
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| PublicationDecade | 2000 |
| PublicationPlace | Cambridge |
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| PublicationYear | 2000 2005 |
| Publisher | Cambridge University Press Cambridge Univ. Press |
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| Snippet | Summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application... This book summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its... |
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| SubjectTerms | Derivat Entscheidung unter Risiko Finance Financial engineering Optionspreistheorie Portfolio-Management Risk Risk assessment Risk management Theorie |
| TableOfContents | Cover -- Half-title -- Title -- Copyright -- Contents -- Foreword -- Preface -- Acknowledgements -- 1 Probability theory: basic notions -- 1.1 Introduction -- 1.2 Probabilities -- 1.2.1 Probability distributions -- 1.2.2 Typical values and deviations -- 1.2.3 Moments and characteristic function -- 1.2.4 Divergence of moments-asymptotic behaviour -- 1.3 Some useful distributions -- 1.3.1 Gaussian distribution -- 1.3.2 Log-normal distribution -- 1.3.3 Lévy distributions and Paretian tails -- 1.3.4 Other distributions (*) -- 1.4 Maximum of random variables-statistics of extremes -- 1.5 Sums of random variables -- 1.5.1 Convolutions -- 1.5.2 Additivity of cumulants and of tail amplitudes -- 1.5.3 Stable distributions and self-similarity -- 1.6 Central limit theorem -- 1.6.1 Convergence to a Gaussian -- 1.6.2 Convergence to a Lévy distribution -- 1.6.3 Large deviations -- 1.6.4 The CLT at work on a simple case -- 1.6.5 Truncated Lévy distributions -- 1.6.6 Conclusion: survival and vanishing of tails -- 1.7 Correlations, dependence and non-stationary models (*) -- 1.7.1 Correlations -- 1.7.2 Non-stationary models and dependence -- 1.8 Central limit theorem for random matrices (*) -- 1.9 Appendix A: non-stationarity and anomalous kurtosis -- 1.10 Appendix B: density of eigenvalues for random correlation matrices -- 1.11 References -- 2 Statistics of real prices -- 2.1 Aim of the chapter -- 2.2 Second-order statistics -- 2.2.1 Variance, volatility and the additive-multiplicative crossover -- 2.2.2 Autocorrelation and power spectrum -- Power spectrum -- 2.3 Temporal evolution of fluctuations -- 2.3.1 Temporal evolution of probability distributions -- The elementary distribution P -- Maximum likelihood -- Convolutions -- Tails, what tails? -- 2.3.2 Multiscaling-Hurst exponent (*) -- 2.4 Anomalous kurtosis and scale fluctuations 4.1.1 Aim of the chapter -- 4.1.2 Trading strategies and efficient markets -- 4.2 Futures and forwards -- 4.2.1 Setting the stage -- 4.2.2 Global financial balance -- 4.2.3 Riskless hedge -- Dividends -- Variable interest rates -- 4.2.4 Conclusion: global balance and arbitrage -- 4.3 Options: definition and valuation -- 4.3.1 Setting the stage -- 4.3.2 Orders of magnitude -- 4.3.3 Quantitative analysis-option price -- Bachelier's Gaussian limit -- Dynamic equation for the option price -- 4.3.4 Real option prices, volatility smile and 'implied' kurtosis -- Stationary distributions and the smile curve -- Non-stationarity and 'implied' kurtosis -- 4.4 Optimal strategy and residual risk -- 4.4.1 Introduction -- 4.4.2 A simple case -- 4.4.3 General case… -- Cumulant corrections to… -- 4.4.4 Global hedging/instantaneous hedging -- 4.4.5 Residual risk: the Black-Scholes miracle -- The 'stop-loss' strategy does not work -- Residual risk to first order in kurtosis -- Stochastic volatility models -- 4.4.6 Other measures of risk-hedging and VaR (*) -- 4.4.7 Hedging errors -- 4.4.8 Summary -- 4.5 Does the price of an option depend on the mean return? -- 4.5.1 The case of non-zero excess return -- 'Risk neutral' probability -- Optimal strategy in the presence of a bias -- 4.5.2 The Gaussian case and the Black-Scholes limit -- Ito calculus -- 4.5.3 Conclusion. Is the price of an option unique? -- 4.6 Conclusion of the chapter: the pitfalls of zero-risk -- 4.7 Appendix D: computation of the conditional mean -- 4.8 Appendix E: binomial model -- 4.9 Appendix F: option price for (suboptimal)… -- 4.10 References -- Some classics -- Market efficiency -- Optimal filters -- Options and futures -- Stochastic differential calculus and derivative pricing -- Option pricing in the presence of residual risk -- Kurtosis and implied cumulants -- Stochastic volatility models 2.5 Volatile markets and volatility markets -- 2.6 Statistical analysis of the forward rate curve (*) -- 2.6.1 Presentation of the data and notations -- 2.6.2 Quantities of interest and data analysis -- 2.6.3 Comparison with the Vasicek model -- 2.6.4 Risk-premium and the… -- The average FRC and value-at-risk pricing -- The anticipated trend and the volatility hump -- 2.7 Correlation matrices (*) -- 2.8 A simple mechanism for anomalous price statistics (*) -- 2.9 A simple model with volatility correlations and tails (*) -- 2.10 Conclusion -- 2.11 References -- Scaling and Fractals in Financial Markets -- The interest rate curve -- Percolation, collective models and self organized criticality -- Other recent market models -- 3 Extreme risks and optimal portfolios -- 3.1 Risk measurement and diversification -- 3.1.1 Risk and volatility -- 3.1.2 Risk of loss and 'Value at Risk' (VaR) -- 3.1.3 Temporal aspects: drawdown and cumulated loss -- Worst low -- Cumulated losses -- Drawdowns -- 3.1.4 Diversification and utility-satisfaction thresholds -- 3.1.5 Conclusion -- 3.2 Portfolios of uncorrelated assets -- 3.2.1 Uncorrelated Gaussian assets -- Effective asset number in a portfolio -- 3.2.2 Uncorrelated 'power-law' assets -- 3.2.3 'Exponential' assets -- 3.2.4 General case: optimal portfolio and VaR (*) -- 3.3 Portfolios of correlated assets -- 3.3.1 Correlated Gaussian fluctuations -- The CAPM and its limitations -- 3.3.2 'Power-law' fluctuations (*) -- 'Tail covariance' -- Optimal portfolio -- 3.4 Optimized trading (*) -- 3.5 Conclusion of the chapter -- 3.6 Appendix C: some useful results -- 3.7 References -- Statistics of drawdowns and extremes -- Portfolio theory and CAPM -- Optimal portfolios in a Lévy world -- Generalization of the covariance to Lévy variables -- 4 Futures and options: fundamental concepts -- 4.1 Introduction 5 Options: some more specific problems -- 5.1 Other elements of the balance sheet -- 5.1.1 Interest rate and continuous dividends -- Systematic drift of the price -- Independence between price increments and interest rates-dividends -- Multiplicative model -- 5.1.2 Interest rates corrections to the hedging strategy -- 5.1.3 Discrete dividends -- 5.1.4 Transaction costs -- 5.2 Other types of options: 'Puts' and 'exotic options' -- 5.2.1 'Put-call' parity -- 5.2.2 'Digital' options -- 5.2.3 'Asian' options -- 5.2.4 'American' options -- American puts -- 5.2.5 'Barrier' options -- Other types of option -- 5.3 The 'Greeks' and risk control -- 5.4 Value-at-risk for general non-linear portfolios (*) -- 5.5 Risk diversification (*) -- 'Portfolio' options and 'exogenous' hedging -- Option portfolio -- 5.6 References -- More on options, exotic options -- Stochastic volatility models and volatility hedging -- Short glossary of financial terms -- Index of symbols -- Index |
| Title | Theory of financial risks : from statistical physics to risk management |
| URI | https://cir.nii.ac.jp/crid/1130000796523445632 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=143920 http://www.econis.eu/PPNSET?PPN=320665151 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780511030987&uid=none |
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