Theory of financial risk and derivative pricing: from statistical physics to risk management
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 2. ed., 1. paperback ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XX, 379 S. graph. Darst. |
| ISBN: | 9780521741866 9780521819169 |
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| 245 | 1 | 0 | |a Theory of financial risk and derivative pricing |b from statistical physics to risk management |c Jean-Philippe Bouchaud and Marc Potters |
| 250 | |a 2. ed., 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XX, 379 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804142803767263232 |
|---|---|
| adam_text | Contents
Foreword page
xiii
Preface
xv
1
Probability theory: basic notions
1
1.1
Introduction
1
1.2
Probability distributions
3
1.3
Typical values and deviations
4
1.4
Moments and characteristic function
6
1.5
Divergence of moments
—
asymptotic behaviour
7
1.6
Gaussian distribution
7
1.7
Log-normal distribution
8
1.8
Levy distributions and
Paretian
tails
10
1.9
Other distributions
(*) 14
1.10
Summary
16
2
Maximum and addition of random variables
17
2.1
Maximum of random variables
17
2.2
Sums of random variables
21
2.2.1
Convolutions
21
2.2.2
Additivity of
cumulants
and of tail amplitudes
22
2.2.3
Stable distributions and self-similarity
23
2.3
Central limit theorem
24
2.3.1
Convergence to a Gaussian
25
2.3.2
Convergence to a Levy distribution
27
2.3.3
Large deviations
28
2.3.4
Steepest descent method and Cramer function
(*) 30
2.3.5
The CLT at work on simple cases
32
2.3.6
Truncated Levy distributions
35
2.3.7
Conclusion: survival and vanishing of tails
36
2.4
From sum to max: progressive dominance of extremes
(*) 37
2.5
Linear correlations and fractional Brownian motion
38
2.6
Summary
40
Contents
Continuous time limit,
Ito
calculus and path integrals
43
3.1
Divisibility and the continuous time limit
43
3.1.1
Divisibility
43
3.1.2
Infinite divisibility
44
3.1.3
Poisson
jump processes
45
3.2
Functions of the Brownian motion and
Ito
calculus
47
3.2.1
Ito s lemma
47
3.2.2
Novikov s formula
49
3.2.3
Stratonovich s prescription
50
3.3
Other techniques
51
3.3.1
Path integrals
51
3.3.2
Girsanov s formula and the Martin-Siggia-Rose trick
(*) 53
3.4
Summary
54
Analysis of empirical data
55
4.1
Estimating probability distributions
55
4.1.1
Cumulative distribution and densities
-
rank histogram
55
4.1.2
Kolmogorov-Smirnov test
56
4.1.3
Maximum likelihood
57
4.1.4
Relative likelihood
59
4.1.5
A general caveat
60
4.2
Empirical moments: estimation and error
60
4.2.1
Empirical mean
60
4.2.2
Empirical variance and MAD
61
4.2.3
Empirical kurtosis
61
4.2.4
Error on the volatility
61
4.3
Correlograms and variograms
62
4.3.1
Variogram
62
4.3.2
Correlogram
63
4.3.3
Hurst exponent
64
4.3.4
Correlations across different time zones
64
4.4
Data with heterogeneous volatilities
66
4.5
Summary
67
Financial products and financial markets
69
5.1
Introduction
69
5.2
Financial products
69
5.2.1
Cash (Interbank market)
69
5.2.2
Stocks
71
5.2.3
Stock indices
72
5.2.4
Bonds
75
5.2.5
Commodities
77
5.2.6
Derivatives
77
Contents
vii
5.3 Financial
markets
79
5.3.1 Market
participants
79
5.3.2 Market
mechanisms
80
5.3.3
Discreteness
81
5.3.4
The order book
81
5.3.5
The bid-ask spread
83
5.3.6
Transaction costs
84
5.3.7
Time zones, overnight, seasonalities
85
5.4
Summary
85
6
Statistics of real prices: basic results
87
6.1
Aim of the chapter
87
6.2
Second-order statistics
90
6.2.1
Price increments vs. returns
90
6.2.2
Autocorrelation and power spectrum
91
6.3
Distribution of returns over different time scales
94
6.3.1
Presentation of the data
95
6.3.2
The distribution of returns
96
6.3.3
Convolutions
101
6.4
Tails, what tails?
102
6.5
Extreme markets
103
6.6
Discussion
104
6.7
Summary
105
7
Non-linear correlations and volatility fluctuations
107
7.1
Non-linear correlations and dependence
107
7.1.1
Non
identical variables
107
7.1.2
A stochastic volatility model
109
7.1.3
GARCHd.l)
110
7.1.4
Anomalous kurtosis
111
7.1.5
The case of infinite kurtosis
113
7.2
Non-linear correlations in financial markets: empirical results
114
7.2.1
Anomalous decay of the
cumulants
114
7.2.2
Volatility correlations and variogram
117
7.3
Models and mechanisms
123
7.3.1
Multifractality and
multirracial
models
(*) 123
7.3.2
The
microstructure
of volatility
125
7.4
Summary
127
8
Skewness
and price-volatility correlations
130
8.1
Theoretical considerations
130
8.1.1
Anomalous skewness of sums of random variables
130
8.1.2
Absolute vs. relative price changes
132
8.1.3
The additive-multiplicative crossover and the q-transformation
134
Viii Contents
8.2
A retarded model
135
8.2.1
Definition and basic properties
135
8.2.2
Skewness in the retarded model
136
8.3
Price-volatility correlations: empirical evidence
137
8.3.1
Leverage effect for stocks and the retarded model
139
8.3.2
Leverage effect for indices
140
8.3.3
Return-volume correlations
141
8.4
The Heston model: a model with volatility fluctuations and skew
141
8.5
Summary
144
9
Cross-correlations
145
9.1
Correlation matrices and principal component analysis
145
9.1.1
Introduction
145
9.1.2
Gaussian correlated variables
147
9.1.3
Empirical correlation matrices
147
9.2
Non-Gaussian correlated variables
149
9.2.1
Sums of
non
Gaussian variables
149
9.2.2
Non-linear transformation of correlated Gaussian variables
150
9.2.3
Copulas
150
9.2.4
Comparison of the two models
151
9.2.5
Multivariate Student distributions
153
9.2.6
Multivariate Levy variables
(*) 154
9.2.7
Weakly
non
Gaussian correlated variables
(*) 155
9.3
Factors and clusters
156
9.3.1
One factor models
156
9.3.2
Multi-factor models
157
9.3.3
Partition around medoids
158
9.3.4
Eigenvector clustering
159
9.3.5
Maximum spanning tree
159
9.4
Summary
160
9.5
Appendix A: central limit theorem for random matrices
161
9.6
Appendix
В
:
density of eigenvalues for random correlation matrices
164
10
Risk measures
168
10.1
Risk measurement and diversification
168
10.2
Risk and volatility
168
10.3
Risk of loss, value at risk (VaR) and expected shortfall
171
10.3.1
Introduction
171
10.3.2
Value-at-risk
172
10.3.3
Expected shortfall
175
10.4
Temporal aspects: drawdown and cumulated loss
176
10.5
Diversification and utility
-
satisfaction thresholds
181
10.6
Summary
184
Contents ix
11 Extreme
correlations and variety
186
11.1
Extreme event correlations
187
11.1.1
Correlations conditioned on large market moves
187
11.1.2
Real data and surrogate data
188
11.1.3
Conditioning on large individual stock returns:
exceedance correlations
189
11.1.4
Tail dependence
191
11.1.5
Tail covariance
(*) 194
11.2
Variety and conditional statistics of the residuals
195
11.2.1
The variety
195
11.2.2
The variety in the one-factor model
196
11.2.3
Conditional variety of the residuals
197
11.2.4
Conditional skewness of the residuals
198
11.3
Summary
199
11.4
Appendix C: some useful results on power-law variables
200
12
Optimal portfolios
202
12.1
Portfolios of uncorrelated assets
202
12.1.1
Uncorrelated Gaussian assets
203
12.1.2
Uncorrelated power-law assets
206
12.1.3
Exponential assets
208
12.1.4
General case: optimal portfolio and VaR
(*) 210
12.2
Portfolios of correlated assets
211
12.2.1
Correlated Gaussian fluctuations
211
12.2.2
Optimal portfolios with non-linear constraints
(*) 215
12.2.3
Power-law fluctuations
—
linear model
(*) 216
12.2.4
Power-law fluctuations
-
Student model
(*) 218
12.3
Optimized trading
218
12.4
Value-at-risk-general non-linear portfolios
(*) 220
12.4.1
Outline of the method: identifying worst cases
220
12.4.2
Numerical test of the method
223
12.5
Summary
224
13
Futures and options: fundamental concepts
226
13.1
Introduction
226
13.1.1
Aim of the chapter
226
13.1.2
Strategies in uncertain conditions
226
13.1.3
Trading strategies and efficient markets
228
13.2
Futures and forwards
231
13.2.1
Setting the stage
231
13.2.2
Global financial balance
232
13.2.3
Riskless hedge
233
13.2.4
Conclusion: global balance and arbitrage
235
χ
Contents
13.3
Options:
definition and valuation
236
13.3.1
Setting the stage
236
13.3.2
Orders of magnitude
238
13.3.3
Quantitative analysis-option price
239
13.3.4
Real option prices, volatility smile and implied
kurtosis
242
13.3.5
The case of an infinite kurtosis
249
13.4
Summary
251
14
Options: hedging and residual risk
254
14.1
Introduction
254
14.2
Optimal hedging strategies
256
14.2.1
A simple case: static hedging
256
14.2.2
The general case and
Δ
hedging
257
14.2.3
Global hedging vs. instantaneous hedging
262
14.3
Residual risk
263
14.3.1
The Black-Scholes miracle
263
14.3.2
The stop-loss strategy does not work
265
14.3.3
Instantaneous residual risk and kurtosis risk
266
14.3.4
Stochastic volatility models
267
14.4
Hedging errors. A variational point of view
268
14.5
Other measures of risk
-
hedging and VaR
(*) 268
14.6
Conclusion of the chapter
271
14.7
Summary
272
14.8
Appendix
D
273
15
Options: the role of drift and correlations
276
15.1
Influence of drift on optimally hedged option
276
15.1.1
A perturbative expansion
276
15.1.2
Risk neutral probability and martingales
278
15.2
Drift risk and delta-hedged options
279
15.2.1
Hedging the drift risk
279
15.2.2
The price of delta-hedged options
280
15.2.3
A general option pricing formula
282
15.3
Pricing and hedging in the presence of temporal correlations
(*) 283
15.3.1
A general model of correlations
283
15.3.2
Derivative pricing with small correlations
284
15.3.3
The case of delta-hedging
285
15.4
Conclusion
285
15.4.1
Is the price of an option unique?
285
15.4.2
Should one always optimally hedge?
286
15.5
Summary
287
15.6
Appendix
E
287
Contents
16
17
18
Options:
the Black and Scholes model
290
16.1
Ito
calculus and the Black-Scholes equation
290
16.1.1
The Gaussian
Bachelier
model
290
16.1.2
Solution and Martingale
291
16.1.3
Time value and the cost of hedging
293
16.1.4
The Log-normal Black-Scholes model
293
16.1.5
General pricing and hedging in a Brownian world
294
16.1.6
The Greeks
295
16.2
Drift and hedge in the Gaussian model
(*)
295
16.2.1
Constant drift
295
16.2.2
Price dependent drift and the Ornstein-Uhlenbeck paradox
296
16.3
The binomial model
297
16.4
Summary
298
Options: some more specific problems
300
17.1
Other elements of the balance sheet
300
17.1.1
Interest rate and continuous dividends
300
17.1.2
Interest rate corrections to the hedging strategy
303
17.1.3
Discrete dividends
303
17.1.4
Transaction costs
304
17.2
Other types of options
305
17.2.1
Put-call parity
305
17.2.2
Digital options
305
17.2.3
Asian options
306
17.2.4
American options
308
17.2.5
Barrier options
(*)
310
17.2.6
Other types of options
312
17.3
The Greeks and risk control
312
17.4
Risk diversification
(*)
313
17.5
Summary
316
Options: minimum variance Monte-Carlo
317
18.1
Plain Monte-Carlo
317
18.1.1
Motivation and basic principle
317
18.1.2
Pricing the forward exactly
319
18.1.3
Calculating the Greeks
320
18.1.4
Drawbacks of the method
322
18.2
An hedged Monte-Carlo method
323
18.2.1
Basic principle of the method
323
18.2.2
A linear parameterization of the price and hedge
324
18.2.3
The Black-Scholes limit
325
18.3
Non
Gaussian models and purely historical option pricing
327
18.4
Discussion and extensions. Calibration
329
X¡¡
Contents
18.5
Summary
331
18.6 Appendix
F:
generating some random variables
331
19
The yield curve
334
19.1
Introduction
334
19.2
The bond market
335
19.3
Hedging bonds with other bonds
335
19.3.1
The general problem
335
19.3.2
The continuous time Gaussian limit
336
19.4
The equation for bond pricing
337
19.4.1
A general solution
339
19.4.2
The Vasicek model
340
19.4.3
Forward rates
341
19.4.4
More general models
341
19.5
Empirical study of the forward rate curve
343
19.5.1
Data and notations
343
19.5.2
Quantities of interest and data analysis
343
19.6
Theoretical considerations
(*) 346
19.6.1
Comparison with the Vasicek model
346
19.6.2
Market price of risk
348
19.6.3
Risk-premium and the
Vö
law
349
19.7
Summary
351
19.8
Appendix G: optimal portfolio of bonds
352
20
Simple mechanisms for anomalous price statistics
355
20.1
Introduction
355
20.2
Simple models for herding and mimicry
356
20.2.1
Herding and percolation
356
20.2.2
Avalanches of opinion changes
357
20.3
Models of feedback effects on price fluctuations
359
20.3.1
Risk-aversion induced crashes
359
20.3.2
A simple model with volatility correlations and tails
363
20.3.3
Mechanisms for long ranged volatility correlations
364
20.4
The Minority Game
366
20.5
Summary
368
Index of most important symbols
372
Index
377
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. New 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.
JEAN-PHILIPPE BOUCHAUD co-founded the company Science
&
Finance, which merged with Capital Fund Management (CFM) in
2000,
where he now supervises the research team with Marc
Potters. He teaches statistical mechanics and finance in various
Grandes
Écoles,
and has worked at CRNS and CEA-Saclay. He was
awarded the CRNS Silver Medal in
іддб.
MARC POTTERS is Head of Research and Chief Portfolio
Manager at CFM. With Jean-Philippe Bouchaud, he supervises
thirty physics Ph.D. researchers and the implementation of their
results into automated trading strategies and risk control models.
He has published numerous articles in the new field of statistical
finance, in particular on Random Matrix Theory applied to
portfolio management.
This is a terrific book. Some
extremely exciting new ideas, ques¬
tions, and techniques are coming
from physics, and many were pio¬
neered by the authors. This book will
teach both academics and praction-
ers a new way of doing finance.
Xavier Gabaix,
MIT
An outstanding and original pres¬
entation of quantitative finance from
a physics perspective.
Nassim Nicholas Taleb,
Empirica LLC,
author of Fooled by Randomness
It is rare to read a quantitative
finance book that has anything new
to say. It is even rarer to find such a
book written by those who know
what they are talking about.
Bouchaud and Potters are two of the
most innovative, imaginative and
experienced researchers in finance.
In this second edition of their
ground-breaking work, they go even
further into their field of econo¬
physics, a field that is changing the
way we view the financial markets.
Each page is packed with more ideas
than most people put into an entire
book. An inspirational book to be
studied carefully and savoured.
Paul Wilmott
Cambridge
UNIVERSITY PRESS
www.cambridge.org
lISBN
978-0-521-74186-6
|
| any_adam_object | 1 |
| author | Bouchaud, Jean-Philippe 1962- Potters, Marc 1969- |
| author_GND | (DE-588)129063053 (DE-588)129063096 |
| author_facet | Bouchaud, Jean-Philippe 1962- Potters, Marc 1969- |
| author_role | aut aut |
| author_sort | Bouchaud, Jean-Philippe 1962- |
| author_variant | j p b jpb m p mp |
| building | Verbundindex |
| bvnumber | BV036130875 |
| classification_rvk | QK 600 SK 980 |
| classification_tum | WIR 160f MAT 902f |
| ctrlnum | (OCoLC)312625586 (DE-599)BVBBV036130875 |
| dewey-full | 658.155 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.155 |
| dewey-search | 658.155 |
| dewey-sort | 3658.155 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., 1. paperback ed. |
| format | Book |
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| id | DE-604.BV036130875 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:35Z |
| institution | BVB |
| isbn | 9780521741866 9780521819169 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020213180 |
| oclc_num | 312625586 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-M347 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-M347 DE-188 |
| physical | XX, 379 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Bouchaud, Jean-Philippe 1962- Verfasser (DE-588)129063053 aut Theory of financial risk and derivative pricing from statistical physics to risk management Jean-Philippe Bouchaud and Marc Potters 2. ed., 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2009 XX, 379 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Finance Financial engineering Risk assessment Risk management Financial Engineering (DE-588)4208404-0 gnd rswk-swf Risikotheorie (DE-588)4135592-1 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Risiko (DE-588)4050129-2 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Kapitalanlage (DE-588)4073213-7 gnd rswk-swf Financial Engineering (DE-588)4208404-0 s Risikomanagement (DE-588)4121590-4 s Optionspreistheorie (DE-588)4135346-8 s 1\p DE-604 Risikotheorie (DE-588)4135592-1 s Kreditmarkt (DE-588)4073788-3 s DE-604 Kapitalanlage (DE-588)4073213-7 s Risiko (DE-588)4050129-2 s Potters, Marc 1969- Verfasser (DE-588)129063096 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020213180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020213180&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bouchaud, Jean-Philippe 1962- Potters, Marc 1969- Theory of financial risk and derivative pricing from statistical physics to risk management Finance Financial engineering Risk assessment Risk management Financial Engineering (DE-588)4208404-0 gnd Risikotheorie (DE-588)4135592-1 gnd Kreditmarkt (DE-588)4073788-3 gnd Risiko (DE-588)4050129-2 gnd Risikomanagement (DE-588)4121590-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| subject_GND | (DE-588)4208404-0 (DE-588)4135592-1 (DE-588)4073788-3 (DE-588)4050129-2 (DE-588)4121590-4 (DE-588)4135346-8 (DE-588)4073213-7 |
| title | Theory of financial risk and derivative pricing from statistical physics to risk management |
| title_auth | Theory of financial risk and derivative pricing from statistical physics to risk management |
| title_exact_search | Theory of financial risk and derivative pricing from statistical physics to risk management |
| title_full | Theory of financial risk and derivative pricing from statistical physics to risk management Jean-Philippe Bouchaud and Marc Potters |
| title_fullStr | Theory of financial risk and derivative pricing from statistical physics to risk management Jean-Philippe Bouchaud and Marc Potters |
| title_full_unstemmed | Theory of financial risk and derivative pricing from statistical physics to risk management Jean-Philippe Bouchaud and Marc Potters |
| title_short | Theory of financial risk and derivative pricing |
| title_sort | theory of financial risk and derivative pricing from statistical physics to risk management |
| title_sub | from statistical physics to risk management |
| topic | Finance Financial engineering Risk assessment Risk management Financial Engineering (DE-588)4208404-0 gnd Risikotheorie (DE-588)4135592-1 gnd Kreditmarkt (DE-588)4073788-3 gnd Risiko (DE-588)4050129-2 gnd Risikomanagement (DE-588)4121590-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| topic_facet | Finance Financial engineering Risk assessment Risk management Financial Engineering Risikotheorie Kreditmarkt Risiko Risikomanagement Optionspreistheorie Kapitalanlage |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020213180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020213180&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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