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EXTREME VALUE METHODS WITH APPLICATIONS TO FINANCE
NOVAK S.Y. wydawnictwo: CRC PRESS, 2011, wydanie I cena netto: 460.00 Twoja cena 437,00 zł + 5% vat - dodaj do koszyka Extreme
Value Methods with Applications to Finance
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes
reported as outliers. Certain textbooks encourage readers to remove outliers—in other
words, to correct reality if it does not fit the model. Recognizing that any model is only
an approximation of reality, statisticians are eager to extract information about unknown
distribution making as few assumptions as possible.
Extreme Value Methods with Applications to Finance concentrates on
modern topics in EVT, such as processes of exceedances, compound Poisson approximation,
Poisson cluster approximation, and nonparametric estimation methods. These topics have not
been fully focused on in other books on extremes.
In addition, the book covers:
Extremes in samples of random size
Methods of estimating extreme quantiles and tail probabilities
Self-normalized sums of random variables
Measures of market risk
Along with examples from finance and insurance to illustrate the methods, Extreme
Value Methods with Applications to Finance includes over 200 exercises, making it
useful as a reference book, self-study tool, or comprehensive course text.
Table of Contents
Introduction
Distribution of Extremes
Methods of Extreme Value Theory
Order Statistics
"Blocks" and "Runs" Approaches
Method of Recurrent Inequalities
Proofs
Maximum of Partial Sums
Erdős–Rényi Maximum of Partial Sums
Basic Inequalities
Limit Theorems for MPS
Proofs
Extremes in Samples of Random Size
Maximum of a Random Number of r.v.s
Number of Exceedances
Length of the Longest Head Run
Long Match Patterns
Poisson Approximation
Total Variation Distance
Method of a Common Probability Space
The Stein Method
Beyond Bernoulli
The Magic Factor
Proofs
Compound Poisson Approximation
Limit Theory
Accuracy of CP Approximation
Proofs
Exceedances of Several Levels
CP Limit Theory
General Case
Accuracy of Approximation
Proofs
Processes of Exceedances
One-level EPPE
Excess Process
Complete Convergence to CP Processes
Proofs
Beyond Compound Poisson
Excess Process
Complete Convergence
Proofs
Statistics of Extremes
Inference on Heavy Tails
Heavy-tailed distributions
Estimation Methods
Tail Index Estimation
Estimation of Extreme Quantiles
Estimation of the Tail Probability
Proofs
Value-at-Risk.
Value-at-Risk and Expected Shortfall
Traditional Methods of VaR Estimation
VaR and ES Estimation from Heavy-Tailed Data
VaR over Different Time Horizons
Technical Analysis of Financial Data
Extremal Index
Preliminaries
Estimation of the Extremal Index
Proofs
Normal Approximation.
Accuracy of Normal Approximation
Stein’s Method
Self-Normalized Sums of r.v.s
Proofs
Lower Bounds
Preliminary Results
Fréchét–Rao–Cramér Inequality
Information Index
Continuity Moduli
Tail Index and Extreme Quantiles
Proofs
Appendix
Probability Distributions
Properties of Distributions
Probabilistic Identities and Inequalities
Distances
Large Deviations
Elements of Renewal Theory
Dependence
Point Processes
Slowly Varying Functions
Useful Identities and Inequalities
References
Index
399 pages, Hardcover
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