Atnaujinkite slapukų nuostatas

Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications [Kietas viršelis]

4.27/5 (339 ratings by Goodreads)
  • Formatas: Hardback, 446 pages, aukštis x plotis x storis: 231x157x28 mm, weight: 748 g, 20 Illustrations
  • Serija: Technical Incerto
  • Išleidimo metai: 30-Jun-2020
  • Leidėjas: STEM Academic Press
  • ISBN-10: 1544508050
  • ISBN-13: 9781544508054
Kitos knygos pagal šią temą:
Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and ApplicationsDidesnis paveikslėlis
  • Formatas: Hardback, 446 pages, aukštis x plotis x storis: 231x157x28 mm, weight: 748 g, 20 Illustrations
  • Serija: Technical Incerto
  • Išleidimo metai: 30-Jun-2020
  • Leidėjas: STEM Academic Press
  • ISBN-10: 1544508050
  • ISBN-13: 9781544508054
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781544508054.html
1 Prologue'
1(4)
2 Glossary, Definitions, And Notations
5(14)
2.1 General Notations and Frequently Used Symbols
5(2)
2.2 Catalogue Raisonne of General & Idiosyncratic concepts
7(12)
2.2.1 Power Law Class B
7(1)
2.2.2 Law of Large Numbers (Weak)
8(1)
2.2.3 The Central Limit Theorem (CLT)
8(1)
2.2.4 Law of Medium Numbers or Preasymptotics
8(1)
2.2.5 Kappa Metric
8(1)
2.2.6 Elliptical Distribution
9(1)
2.2.7 Statistical independence
9(1)
2.2.8 Stable (Levy stable) Distribution
10(1)
2.2.9 Multivariate Stable Distribution
10(1)
2.2.10 Karamata Point
10(1)
2.2.11 Subexponentialiry
10(1)
2.2.12 Student T as Proxy
11(1)
2.2.13 Citation Ring
11(1)
2.2.14 Rent seeking in academia
12(1)
2.2.15 Pseudo-empiricism or Pinker Problem
12(1)
2.2.16 Preasymptotics
12(1)
2.2.17 Stochasticizing
13(1)
2.2.18 Value at Risk, Conditional VaR
13(1)
2.2.19 Skin in the Game
13(1)
2.2.20 MS Plot
14(1)
2.2.21 Maximum Domain of Attraction, MDA
14(1)
2.2.22 Substitution of Integral in the psychology literature
14(1)
2.2.23 Inseparability of Probability (another common error)
15(1)
2.2.24 Wittgenstein's Ruler
15(1)
2.2.25 Black Swans
15(1)
2.2.26 The Empirical Distribution is Not Empirical
16(1)
2.2.27 The Hidden Tail
17(1)
2.2.28 Shadow Moment
17(1)
2.2.29 Tail Dependence
17(1)
2.2.30 Metaprobability
17(1)
2.2.31 Dynamic Hedging
18(1)
I FAT TAILS AND THEIR EFFECTS, AN INTRODUCTION
19(100)
3 A Non-Technical Overview - The Darwin Collece Lecture*‡
21(44)
3.1 On the Difference Between Thin and Thick Tails
21(2)
3.2 Tail Wagging Dogs: An Intuition
23(2)
3.3 A (More Advanced) Categorization and Its Consequences
25(5)
3.4 The Main Consequences and How They Link to the Book
30(11)
3.4.1 Forecasting
37(2)
3.4.2 The Law of Large Numbers
39(2)
3.5 Epistemology and Inferential Asymmetry
41(5)
3.6 Naive Empiricism: Ebola Should Not Be Compared to Falls from Ladders
46(4)
3.6.1 How some multiplicative risks scale
49(1)
3.7 Primer on Power Laws (almost without mathematics)
50(3)
3.8 Where Are the Hidden Properties?
53(3)
3.9 Bayesian Schmayesian
56(1)
3.10 X vs F(X): exposures to X confused with knowledge about X
57(3)
3.11 Ruin and Path Dependence
60(3)
3.12 What To Do?
63(2)
4 Univariate Fat Tails, Level 1, Finite Moments†
65(24)
4.1 A Simple Heuristic to Create Mildly Fat Tails
65(5)
4.1.1 A Variance-preserving heuristic
67(1)
4.1.2 Fattening of Tails With Skewed Variance
68(2)
4.2 Does Stochastic Volatility Generate Power Laws?
70(1)
4.3 The Body, The Shoulders, and The Tails
71(4)
4.3.1 The Crossovers and Tunnel Effect
72(3)
4.4 Fat Tails, Mean Deviation and the Rising Norms
75(11)
4.4.1 The Common Errors
75(1)
4.4.2 Some Analytics
76(2)
4.4.3 Effect of Fatter Tails on the "efficiency" of STD vs MD
78(1)
4.4.4 Moments and The Power Mean Inequality
79(3)
4.4.5 Comment: Why we should retire standard deviation, now!
82(4)
4.5 Visualizing the Effect of Rising p on Iso-Norms
86(3)
5 Level 2: Subexponentials and power laws
89(16)
5.0.1 Revisiting the Rankings
89(2)
5.0.2 What is a Borderline Probability Distribution?
91(1)
5.0.3 Let Us Invent a Distribution
92(1)
5.1 Level 3: Scalability and Power Laws
93(3)
5.1.1 Scalable and Nonscalable, A Deeper View of Fat Tails
93(2)
5.1.2 Grey Swans
95(1)
5.2 Some Properties of Power Laws
96(2)
5.2.1 Sums of variables
96(1)
5.2.2 Transformations
97(1)
5.3 Bell Shaped vs Non Bell Shaped Power Laws
98(1)
5.4 Interpolative powers of Power Laws: An Example
99(1)
5.5 Super-Fat Tails: The Log-Pareto Distribution
99(1)
5.6 Pseudo-Stochastic Volatility: An investigation
100(5)
6 Thick Tails In Hicher Dimensions†
105(14)
6.1 Thick Tails in Higher Dimension, Finite Moments
106(2)
6.2 Joint Fat-Tailedness and Ellipticality of Distributions
108(2)
6.3 Multivariate Student T
110(2)
6.3.1 Ellipticality and Independence under Thick Tails
111(1)
6.4 Fat Tails and Mutual Information
112(2)
6.5 Fat Tails and Random Matrices, a Rapid Interlude
114(1)
6.6 Correlation and Undefined Variance
114(2)
6.7 Fat Tailed Residuals in Linear Regression Models
116(3)
A Special Cases Of Thick Tails
119(6)
A.1 Multimodality and Thick Tails, or the War and Peace Model
119(4)
A.2 Transition Probabilities: What Can Break Will Break
123(2)
II THE LAW OF MEDIUM NUMBERS
125(48)
7 Limit Distributions, A Con Soli Dation*†
127(16)
7.1 Refresher: The Weak and Strong LLN
127(2)
7.2 Central Limit in Action
129(2)
7.2.1 The Stable Distribution
129(1)
7.2.2 The Law of Large Numbers for the Stable Distribution
130(1)
7.3 Speed of Convergence of CLT: Visual Explorations
131(4)
7.3.1 Fast Convergence: the Uniform Dist
131(1)
7.3.2 Semi-slow convergence: the exponential
132(1)
7.3.3 The slow Pareto
133(2)
7.3.4 The half-cubic Pareto and its basin of convergence
135(1)
7.4 Cumulants and Convergence
135(2)
7.5 Technical Refresher: Traditional Versions of CLT
137(1)
7.6 The Law of Large Numbers for Higher Moments
138(3)
7.6.1 Higher Moments
138(3)
7.7 Mean deviation for a Stable Distributions
141(2)
8 How much data do you need? An operational metric for fat-Tailedness‡
143(18)
8.1 Introduction and Definitions
144(2)
8.2 The Metric
146(2)
8.3 Stable Basin of Convergence as Benchmark
148(3)
8.3.1 Equivalence for Stable distributions
149(1)
8.3.2 Practical significance for sample sufficiency
149(2)
8.4 Technical Consequences
151(1)
8.4.1 Some Oddities With Asymmetric Distributions
151(1)
8.4.2 Rate of Convergence of a Student T Distribution to the Gaussian Basin
151(1)
8.4.3 The Lognormal is Neither Thin Nor Fat Tailed
152(1)
8.4.4 Can Kappa Be Negative?
152(1)
8.5 Conclusion and Consequences
152(2)
8.5.1 Portfolio Pseudo-Stabilization
153(1)
8.5.2 Other Aspects of Statistical Inference
154(1)
8.5.3 Final comment
154(1)
8.6 Appendix, Derivations, and Proofs
154(7)
8.6.1 Cubic Student T (Gaussian Basin)
154(2)
8.6.2 Lognormal Sums
156(2)
8.6.3 Exponential
158(1)
8.6.4 Negative Kappa, Negative Kurtosis
159(2)
9 Extreme Values And Hidden Tails*†
161(12)
9.1 Preliminary Introduction to EVT
161(6)
9.1.1 How Any Power Law Tail Leads to Fr6chet
163(1)
9.1.2 Gaussian Case
164(2)
9.1.3 The Picklands-Balkema-de Haan Theorem
166(1)
9.2 The Invisible Tail for a Power Law
167(3)
9.2.1 Comparison with the Normal Distribution
170(1)
9.3 Appendix: The Empirical Distribution is Not Empirical
170(3)
B Growth Rate And Outcome Are Not In The Same Distribution Class
173(4)
B.1 The Puzzle
173(3)
B.2 Pandemics are really Fat Tailed
176(1)
C The Large Deviation Principle, In Brief
177(4)
D Calibrating Under Paretianity
181(18)
D.1 Distribution of the sample tail Exponent
183(2)
10 "It is what it is": diagnosing the SP500†
185(14)
10.1 Paretianity and Moments
185(2)
10.2 Convergence Tests
187(10)
10.2.1 Test 1: Kurtosis under Aggregation
187(1)
10.2.2 Maximum Drawdowns
188(1)
10.2.3 Empirical Kappa
189(1)
10.2.4 Test 2: Excess Conditional Expectation
190(2)
10.2.5 Test 3iJnstability of 4th moment
192(1)
10.2.6 Test 4: MS Plot
192(2)
10.2.7 Records and Extrema
194(3)
10.2.8 Asymmetry right-left tail
197(1)
10.3 Conclusion: It is what it is
197(2)
E The Problem With Econometrics
199(8)
E.1 Performance of Standard Parametric Risk Estimators
200(2)
E.2 Performance of Standard NonParametric Risk Estimators
202(5)
F Machine Learning Considerations
207(4)
F.0.1 Calibration via Angles
209(2)
III PREDICTIONS, FORECASTING, AND UNCERTAINTY
211(38)
11 Probability Calibration Under Fat Tails‡
213(22)
11.1 Continuous vs. Discrete Payoffs: Definitions and Comments
214(5)
11.1.1 Away from the Verbalistic
215(3)
11.1.2 There is no defined "collapse", "disaster", or "success" under fat tails
218(1)
11.2 Spurious overestimation of tail probability in psychology
219(6)
11.2.1 Thin tails
220(1)
11.2.2 Fat tails
220(1)
11.2.3 Conflations
221(3)
11.2.4 Distributional Uncertainty
224(1)
11.3 Calibration and Miscalibration
225(1)
11.4 Scoring Metrics
225(4)
11.4.1 Deriving Distributions
228(1)
11.5 Non-Verbalistic Payoff Functions/Machine Learning
229(3)
11.6 Conclusion
232(1)
11.7 Appendix: Proofs and Derivations
232(3)
11.7.1 Distribution of Binary Tally pW(n)
232(1)
11.7.2 Distribution of the Brier Score
233(2)
12 Election Predictions As Martingales: An Arbitrage Approach‡
235(14)
12.0.1 Main results
237(1)
12.0.2 Organization
238(2)
12.0.3 A Discussion on Risk Neutrality
240(1)
12.1 The Bachelier-Style valuation
240(2)
12.2 Bounded Dual Martingale Process
242(3)
12.3 Relation to De Finetti's Probability Assessor
245(1)
12.4 Conclusion and Comments
245(4)
IV INEQUALITY ESTIMATORS UNDER FAT TAILS
249(36)
13 Gini Estimation Under Infinite Variance‡
251(20)
13.1 Introduction
251(4)
13.2 Asymptotics of the Nonparametric Estimator under Irifinite Variance
255(3)
13.2.1 A Quick Recap on a-Stable Random Variables
256(1)
13.2.2 The a-Stable Asymptotic Limit of the Gini Index
257(1)
13.3 The Maximum Likelihood Estimator
258(1)
13.4 A Paretian illustration
259(3)
13.5 Small Sample Correction
262(3)
13.6 Conclusions
265(6)
14 On The Super-Additivity And Estimation Biases Of Quantile Contributions‡
271(14)
14.1 Introduction
271(2)
14.2 Estimation For Unmixed Pareto-Tailed Distributions
273(3)
14.2.1 Bias and Convergence
273(3)
14.3 An Inequality About Aggregating Inequality
276(3)
14.4 Mixed Distributions For The Tail Exponent
279(3)
14.5 A Larger Total Sum is Accompanied by Increases in jc9
282(1)
14.6 Conclusion and Proper Estimation of Concentration
282(3)
14.6.1 Robust methods and use of exhaustive data
283(1)
14.6.2 How Should We Measure Concentration?
283(2)
V SHADOW MOMENTS PAPERS
285(32)
15 Shadow Moments Of Apparently Infinite-Mean Phenomena‡
287(10)
15.1 Introduction
287(1)
15.2 The dual Distribution
288(2)
15.3 Back to Y: the shadow mean (or population mean)
290(3)
15.4 Comparison to Other Methods
293(1)
15.5 Applications
294(3)
16 On The Tail Risk Of Violent Conflict (With P. Cirillo)‡
297(20)
16.1 Introduction/Summary
297(3)
16.2 Summary statistical discussion
300(2)
16.2.1 Results
300(1)
16.2.2 Conclusion
301(1)
16.3 Methodological Discussion
302(4)
16.3.1 Rescaling Method
302(1)
16.3.2 Expectation by Conditioning (less rigorous)
303(1)
16.3.3 Reliability of Data and Effect on Tail Estimates
304(1)
16.3.4 Definition of An "Event"
305(1)
16.3.5 Missing Events
306(1)
16.3.6 Survivorship Bias
306(1)
16.4 Data analysis
306(6)
16.4.1 Peaks over Threshold
307(1)
16.4.2 Gaps in Series and Autocorrelation
308(1)
16.4.3 Tail Analysis
309(2)
16.4.4 An Alternative View on Maxima
311(1)
16.4.5 Fuu Data Analysis
311(1)
16.5 Additional robustness and reliability tests
312(2)
16.5.1 Bootstrap for the GPD
312(1)
16.5.2 Perturbation Across Bounds of Estimates
313(1)
16.6 Conclusion: is the world more unsafe than it seems?
314(2)
16.7 Acknowledgments
316(1)
G WHAT ARE THE CHANCES OF A THIRD WORLD WAR?*†
317(4)
VI METAPROBABILITY PAPERS
321(34)
17 How Thick Tails Emerge From Recursive Epistemic Uncertainty†
323(12)
17.1 Methods and Derivations
324(7)
17.1.1 Layering Uncertainties
324(1)
17.1.2 Higher Order Integrals in the Standard Gaussian Case
325(4)
17.1.3 Effect on Small Probabilities
329(2)
17.2 Regime 2: Cases of decaying parameters a(n)
331(2)
17.2.1 Regime 2-a;"Bleed" of Higher Order Error
331(1)
17.2.2 Regime 2-b; Second Method, a Non Multiplicative Error Rate
332(1)
17.3 Limit Distribution
333(2)
18 Stochastic Tail Exponent For Asymmetric Power Laws†
335(10)
18.1 Background
336(1)
18.2 One Tailed Distributions with Stochastic Alpha
336(3)
18.2.1 General Cases
336(1)
18.2.2 Stochastic Alpha Inequality
337(1)
18.2.3 Approximations for the Class B
338(1)
18.3 Sums of Power Laws
339(1)
18.4 Asymmetric Stable Distributions
340(1)
18.5 Pareto Distribution with lognormally distributed α
341(1)
18.6 Pareto Distribution with Gamma distributed Alpha
342(1)
18.7 The Bounded Power Law in Cirillo and Taleb (2016)
342(1)
18.8 Additional Comments
343(1)
18.9 Acknowledgments
343(2)
19 Meta-Distribution Of P-Values And P-Hackinc‡
345(10)
19.1 Proofs and derivations
347(4)
19.2 Inverse Power of Test
351(1)
19.3 Application and Conclusion
352(3)
H SOME CONFUSIONS IN BEHAVIORAL ECONOMICS
355(6)
H.1 Case Study: How the myopic loss aversion is misspecified
355(6)
VII Option Trading And Pricing Under Fat Tails
361(58)
20 Financial Theory's Failures With Option Pricing†
363(4)
20.1 Bachelier not Black-Scholes
363(4)
20.1.1 Distortion from Idealization
364(2)
20.1.2 The Actual Replication Process
366(1)
20.1.3 Failure: How Hedging Errors Can Be Prohibitive
366(1)
21 Unique Option Pricing Measure (No Dynamic Hedging/Complete Markets)‡
367(8)
21.1 Background
367(2)
21.2 Proof
369(4)
21.2.1 Case 1: Forward as risk-neutral measure
369(1)
21.2.2 Derivations
369(4)
21.3 Case where the Forward is not risk neutral
373(1)
21.4 Comment
373(2)
22 Option Traders Never Use The Black-Scholes-Merton Formula‡
375(16)
22.1 Breaking the Chain of Transmission
375(1)
22.2 Introduction/Summary
376(3)
22.2.1 Black-Scholes was an argument
376(3)
22.3 Myth 1: Traders did not price options before BSM
379(1)
22.4 Methods and Derivations
380(4)
22.4.1 Option formulas and Delta Hedging
383(1)
22.5 Myth 2: Traders Today use Black-Scholes
384(1)
22.5.1 When do we value?
385(1)
22.6 On the Mathematical Impossibility of Dynamic Hedging
385(6)
22.6.1 The (confusing) Robustness of the Gaussian
387(1)
22.6.2 Order Flow and Options
388(1)
22.6.3 Bachelier-Thorp
388(3)
23 Option Pricing Under Power Laws: A Robust Heuristic*‡
391(8)
23.1 Introduction
392(1)
23.2 Call Pricing beyond the Karamata constant
392(4)
23.2.1 First approach, S is in the regular variation class
393(1)
23.2.2 Second approach, S has geometric returns in the regular variation class
394(2)
23.3 Put Pricing
396(1)
23.4 Arbitrage Boundaries
397(1)
23.5 Comments
398(1)
24 Four Mistakes In Quantitative Finance*‡
399(6)
24.1 Conflation of Second and Fourth Moments
399(1)
24.2 Missing Jensen's Inequality in Analyzing Option Returns
400(1)
24.3 The Inseparability of Insurance and Insured
401(1)
24.4 The Necessity of a Numeraire in Finance
402(1)
24.5 Appendix (Betting on Tails of Distribution)
402(3)
25 Tail Risk Constraints And Maximum Entropy (w. D & H. Ceman)‡
405(14)
25.1 Left Tail Risk as the Central Portfolio Constraint
405(3)
25.1.1 The Barbell as seen by E.T. Jaynes
408(1)
25.2 Revisiting the Mean Variance Setting
408(2)
25.2.1 Analyzing the Constraints
409(1)
25.3 Revisiting the Gaussian Case
410(2)
25.3.1 A Mixture of Two Normals
411(1)
25.4 Maximum Entropy
412(5)
25.4.1 Case A: Constraining the Global Mean
413(1)
25.4.2 Case B: Constraining the Absolute Mean
414(1)
25.4.3 Case C: Power Laws for the Right Tail
415(1)
25.4.4 Extension to a Multi-Period Setting: A Comment
415(2)
25.5 Comments and Conclusion
417(1)
25.6 Appendix/Proofs
417(2)
Bibliography and Index 419