Springer- Statistical Mechanics of Financial Markets

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Contents
1. Introduction .............................................. 1
1.1 Motivation ............................................ 1
1.2 WhyPhysicists?WhyModelsofPhysics? ................. 4
1.3 PhysicsandFinance–Historical ......................... 6
1.4 Aimsof thisBook ...................................... 8
2. Basic Information on Capital Markets .................... 13
2.1 Risk .................................................. 13
2.2 Assets ................................................ 13
2.3 Three ImportantDerivatives............................. 15
2.3.1 ForwardContracts................................ 16
2.3.2 FuturesContract................................. 16
2.3.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Derivative Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 MarketActors ......................................... 20
2.6 PriceFormationatOrganizedExchanges .................. 21
2.6.1 OrderTypes..................................... 21
2.6.2 Price Formation by Auction . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.3 Continuous Trading:
TheXETRAComputerTradingSystem............. 23
3. Random Walks in Finance and Physics ................... 27
3.1 ImportantQuestions.................................... 27
3.2 Bachelier’s “Th′ eorie de la Sp′ eculation”.................... 28
3.2.1 Preliminaries .................................... 28
3.2.2 Probabilities in Stock Market Operations . . . . . . . . . . . . 32
3.2.3 Empirical Data on Successful Operations
inStockMarkets ................................. 39
3.2.4 Biographical Information
on Louis Bachelier (1870–1946) . . . . . . . . . . . . . . . . . . . . 40
3.3 Einstein’sTheoryofBrownianMotion .................... 41
3.3.1 Osmotic Pressure and Di?usion in Suspensions . . . . . . . 41
3.3.2 BrownianMotion................................. 43
3.4 Experimental Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Financial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Perrin’s Observations of Brownian Motion . . . . . . . . . . . 46
3.4.3 One-Dimensional Motion of Electronic Spins . . . . . . . . . 47
4. The Black–Scholes Theory of Option Prices ............... 51
4.1 ImportantQuestions.................................... 51
4.2 AssumptionsandNotation............................... 52
4.2.1 Assumptions..................................... 52
4.2.2 Notation ........................................ 53
4.3 Prices forDerivatives ................................... 53
4.3.1 Forward Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2 FuturesPrice ................................... 55
4.3.3 Limits on Option Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4 Modeling Fluctuations of Financial Assets . . . . . . . . . . . . . . . . . 58
4.4.1 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.2 The Standard Model of Stock Prices . . . . . . . . . . . . . . . . 67
4.4.3 The It? oLemma .................................. 68
4.4.4 Log-normal Distributions for Stock Prices . . . . . . . . . . . 70
4.5 Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.1 The Black–Scholes Di?erential Equation . . . . . . . . . . . . . 72
4.5.2 Solution of the Black–Scholes Equation . . . . . . . . . . . . . 75
4.5.3 Risk-NeutralValuation............................ 80
4.5.4 American Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.5 TheGreeks...................................... 83
4.5.6 Synthetic Replication of Options . . . . . . . . . . . . . . . . . . . 87
4.5.7 Implied Volatility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.8 Volatility Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5. Scaling in Financial Data and in Physics .................. 101
5.1 ImportantQuestions.................................... 101
5.2 StationarityofFinancialMarkets......................... 102
5.3 Geometric Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.1 PriceHistories ................................... 106
5.3.2 Statistical Independence of Price Fluctuations . . . . . . . 106
5.3.3 Statistics of Price Changes of Financial Assets . . . . . . . 111
5.4 Pareto Laws and L′ evyFlights............................ 120
5.4.1 De?nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.4.2 The Gaussian Distribution and the Central Limit The-
orem............................................ 123
5.4.3 L′ evyDistributions................................ 126
5.4.4 Non-stable Distributions with Power Laws . . . . . . . . . . . 129
5.5 Scaling, L′ evy Distributions,
and L′ evy Flights in Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.5.1 Criticality and Self-Organized Criticality,
Di?usionandSuperdi?usion ....................... 131
5.5.2 Micelles ......................................... 133
5.5.3 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.5.4 TheDynamicsof theHumanHeart................. 137
5.5.5 Amorphous Semiconductors and Glasses . . . . . . . . . . . . . 138
5.5.6 Superposition of Chaotic Processes . . . . . . . . . . . . . . . . . 141
5.5.7 Tsallis Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.6 New Developments: Non-stable Scaling, Temporal
and Interasset Correlations in Financial Markets . . . . . . . . . . . 146
5.6.1 Non-stable Scaling in Financial Asset Returns . . . . . . . . 147
5.6.2 TheBreadthof theMarket ........................ 151
5.6.3 Non-linearTemporalCorrelations .................. 154
5.6.4 Stochastic Volatility Models . . . . . . . . . . . . . . . . . . . . . . . 159
5.6.5 Cross-Correlations inStockMarkets ................ 161
6. Turbulence and Foreign Exchange Markets ............... 173
6.1 ImportantQuestions.................................... 173
6.2 TurbulentFlows........................................ 173
6.2.1 Phenomenology .................................. 174
6.2.2 StatisticalDescriptionofTurbulence................ 178
6.2.3 Relation to Non-extensive Statistical Mechanics . . . . . . 181
6.3 ForeignExchangeMarkets............................... 182
6.3.1 WhyForeignExchangeMarkets?................... 182
6.3.2 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
6.3.3 StochasticCascadeModels ........................ 189
6.3.4 The Multifractal Interpretation . . . . . . . . . . . . . . . . . . . . 191
7. Derivative Pricing Beyond Black–Scholes ................. 197
7.1 ImportantQuestions.................................... 197
7.2 An Integral Framework for Derivative Pricing . . . . . . . . . . . . . . 197
7.3 ApplicationtoForwardContracts ........................ 199
7.4 OptionPricing(EuropeanCalls) ......................... 200
7.5 MonteCarloSimulations ................................ 204
7.6 Option Pricing in a Tsallis World . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.7 Path Integrals: Integrating the Fat Tails
into Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.8 Path Integrals: Integrating Path Dependence
into Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
8. Microscopic Market Models .............................. 221
8.1 ImportantQuestions.................................... 221
8.2 AreMarketsE?cient? .................................. 222
8.3 ComputerSimulationofMarketModels ................... 226
8.3.1 TwoClassicalExamples........................... 226
8.3.2 Recent Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.4 TheMinorityGame .................................... 246
8.4.1 TheBasicMinorityGame ......................... 247
8.4.2 A Phase Transition in the Minority Game . . . . . . . . . . . 249
8.4.3 RelationtoFinancialMarkets...................... 250
8.4.4 Spin Glasses and an Exact Solution . . . . . . . . . . . . . . . . . 252
8.4.5 Extensionsof theMinorityGame................... 255
9. Theory of Stock Exchange Crashes ....................... 259
9.1 ImportantQuestions.................................... 259
9.2 Examples.............................................. 260
9.3 EarthquakesandMaterialFailure ........................ 264
9.4 StockExchangeCrashes................................. 270
9.5 WhatCausesCrashes?.................................. 276
9.6 AreCrashesRational? .................................. 278
9.7 WhatHappensAfteraCrash? ........................... 279
9.8 ARichterScale forFinancialMarkets..................... 285

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关键词：Statistical statistica Mechanics financial statistic Statistical financial Markets Mechanics Springer

10. Risk Management ........................................ 289
10.1 ImportantQuestions.................................... 289
10.2What isRisk?.......................................... 290
10.3 Measures of Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
10.3.1 Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
10.3.2 Generalizations of Volatility and Moments . . . . . . . . . . . 293
10.3.3 StatisticsofExtremalEvents ...................... 295
10.3.4 ValueatRisk .................................... 297
10.3.5 CoherentMeasuresofRisk ........................ 303
10.3.6 Expected Shortfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
10.4 TypesofRisk.......................................... 308
10.4.1 Market Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
10.4.2 CreditRisk...................................... 308
10.4.3 OperationalRisk................................. 311
10.4.4 Liquidity Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
10.5 RiskManagement ...................................... 314
10.5.1 Risk Management Requires a Strategy . . . . . . . . . . . . . . 314
10.5.2 LimitSystems ................................... 315
10.5.3 Hedging......................................... 316
10.5.4 PortfolioInsurance ............................... 317
10.5.5 Diversification ................................... 318
10.5.6 StrategicRiskManagement........................ 323
11. Economic and Regulatory Capital
for Financial Institutions ................................. 325
11.1 ImportantQuestions.................................... 325
11.2 Economic Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
11.2.1 WhatDeterminesEconomicCapital? ............... 326
11.2.2 How Calculate Economic Capital? . . . . . . . . . . . . . . . . . . 327
11.2.3 How Allocate Economic Capital? . . . . . . . . . . . . . . . . . . . 328
11.2.4 Economic Capital as a Management Tool . . . . . . . . . . . . 331
11.3 TheRegulatoryFramework.............................. 333
11.3.1 WhyBankingRegulation?......................... 333
11.3.2 Risk-BasedCapitalRequirements .................. 334
11.3.3 Basel I:RegulationofCreditRisk .................. 336
11.3.4 InternalModels .................................. 338
11.3.5 Basel II: The New International Capital
AdequacyFramework............................. 341
11.3.6 Outlook:Basel IIIandBasel IV.................... 358
Appendix ..................................................... 359
Notes and References ......................................... 364
Index ......................................................... 375