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Financial Modeling Under Non-Gaussian Distributions 2007 ed. [Kõva köide]

  • Formaat: Hardback, 541 pages, kõrgus x laius: 235x156 mm, kaal: 2110 g, XVIII, 541 p., 1 Hardback
  • Sari: Springer Finance
  • Ilmumisaeg: 23-Nov-2006
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1846284198
  • ISBN-13: 9781846284199
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  • Formaat: Hardback, 541 pages, kõrgus x laius: 235x156 mm, kaal: 2110 g, XVIII, 541 p., 1 Hardback
  • Sari: Springer Finance
  • Ilmumisaeg: 23-Nov-2006
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1846284198
  • ISBN-13: 9781846284199
Teised raamatud teemal:
Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve, associated with the Gaussian or normal distribution. Indeed, the use of Gaussian models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses or mispriced derivative products. Consequently, non-Gaussian models and models based on processes with jumps, are gaining popularity among financial market practitioners.Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models or black boxes. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates. The authors have taken care to make the material accessible to anyone with a basic knowledge of statistics, calculus and probability, while at the same time preserving the mathematical rigor and complexity of the original models. This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.

This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.

Arvustused

From the reviews:









"Financial Modeling Under Non-Gaussian Distributions is thus very welcome as it provides an accessible and easy-to-understand treatment of a broad range of topics, including core material to more advanced techniques on the subject of capturing non-Gaussian properties in the distributions of asset returns. Financial Modeling Under Non-Gaussian Distributions is a very accessible textbook that covers a wide range of topics. The authors define their target readers as specialized master and Ph.D. students, as well as financial industry practitioners." (Stephan Suess, Financial Markets and Portfolio Management, Vol. 22, 2008)



"This book is written for non-mathematicians who want to model financial market prices. ... It targets practioners in the financial industry. It is suitable for use as core text for students in empirical finance, financial econometrics and financial derivatives. It is useful for mathematician who want to know more about their mathematical tools are applied in finance." (Klaus Ehemann, Zentralblatt MATH, Vol. 1138 (16), 2008)

Part I Financial Markets and Financial Time Series
1 Introduction
3(4)
1.1 Financial markets and financial time series
3(1)
1.2 Econometric modeling of asset returns
4(1)
1.3 Applications of non-Gaussian econometrics
5(1)
1.4 Option pricing with non-Gaussian distributions
5(2)
2 Statistical Properties of Financial Market Data
7(26)
2.1 Definitions of returns
7(3)
2.1.1 Simple returns
8(1)
2.1.2 Log-returns
8(1)
2.1.3 Stylized facts
9(1)
2.2 Distribution of returns
10(11)
2.2.1 Moments of a random variable
10(4)
2.2.2 Empirical moments
14(2)
2.2.3 Testing for normality
16(5)
2.3 Time dependency
21(5)
2.3.1 Serial correlation in returns
22(1)
2.3.2 Serial correlation in volatility
23(2)
2.3.3 Volatility asymmetry
25(1)
2.3.4 Time-varying higher moments
26(1)
2.4 Linear dependence across returns
26(5)
2.4.1 Pearson's correlation coefficient
27(1)
2.4.2 Test for equality of two correlation coefficients
28(2)
2.4.3 Test for equality of two correlation matrices
30(1)
2.5 Multivariate higher moments
31(2)
2.5.1 Multivariate co-skewness and co-kurtosis
31(1)
2.5.2 Computing moments of portfolio returns
32(1)
3 Functioning of Financial Markets and Theoretical Models for Returns
33(46)
3.1 Functioning of financial markets
34(5)
3.1.1 Organization of financial markets
34(3)
3.1.2 Examples of orders
37(2)
3.1.3 Components of the bid-ask spread
39(1)
3.2 Mandelbrot and the stable distribution
39(5)
3.2.1 A puzzling result
40(1)
3.2.2 Stable distribution
41(3)
3.3 Clark's subordination model
44(4)
3.3.1 The idea of the model
44(2)
3.3.2 The density of returns under subordination
46(2)
3.4 A bivariate mixture-of-distribution model for return and volume
48(14)
3.4.1 A microstructure model for information arrivals
48(5)
3.4.2 Implications of the mixture of distributions hypothesis
53(4)
3.4.3 Testing the mixture of distribution hypothesis
57(4)
3.4.4 Extensions
61(1)
3.5 A model of prices and quotes in a quote-driven market
62(17)
3.5.1 A model based on the trade flow
63(3)
3.5.2 Estimating the parameters
66(2)
3.5.3 The quote process
68(5)
3.5.4 Extension to the liquidation of a large portfolio
73(6)
Part II Econometric Modeling of Asset Returns
4 Modeling Volatility
79(64)
4.1 Volatility at lower frequencies
79(2)
4.2 ARCH model
81(3)
4.2.1 Forecasting
81(1)
4.2.2 Kurtosis of an ARCH model
82(1)
4.2.3 Testing for ARCH effects
82(1)
4.2.4 ARCH-in-mean model
83(1)
4.2.5 Illustration
84(1)
4.3 GARCH model
84(10)
4.3.1 Forecasting
88(1)
4.3.2 Integrated GARCH model
89(1)
4.3.3 Estimation
89(3)
4.3.4 Testing for GARCH effects
92(1)
4.3.5 Software to estimate ARCH and GARCH models
92(1)
4.3.6 Illustration
93(1)
4.4 Asymmetric GARCH models
94(5)
4.4.1 EGARCH model
94(1)
4.4.2 TGARCH model
95(1)
4.4.3 GJR model
95(1)
4.4.4 Cox-Box transform
95(1)
4.4.5 News impact curve
96(1)
4.4.6 Partially non-parametric estimation
96(1)
4.4.7 Testing for asymmetric effects
97(2)
4.4.8 Illustration
99(1)
4.5 GARCH model with jumps
99(9)
4.5.1 A model with time-varying jump intensity
101(4)
4.5.2 An empirical illustration
105(3)
4.6 Aggregation of GARCH processes
108(7)
4.6.1 Temporal aggregation
109(4)
4.6.2 Cross-sectional aggregation
113(1)
4.6.3 Estimation of the weak GARCH process
114(1)
4.7 Stochastic volatility
115(3)
4.7.1 From GARCH models to stochastic volatility models
115(2)
4.7.2 Estimation of the discrete time SV model
117(1)
4.8 Realized volatility
118(25)
4.8.1 The difficulty to disentangle jumps
119(4)
4.8.2 Quadratic variation
123(1)
4.8.3 Power variation
124(2)
4.8.4 Bipower variation
126(2)
4.8.5 Estimation over finite time intervals
128(7)
4.8.6 Realized covariance
135(6)
4.8.7 Further related results
141(2)
5 Modeling Higher Moments
143(52)
5.1 The general problem
144(8)
5.1.1 Higher moments of a GARCH process
145(3)
5.1.2 Quasi Maximum Likelihood Estimation
148(3)
5.1.3 The existence of distribution with given moments
151(1)
5.2 Distributions with higher moments
152(25)
5.2.1 Semi-parametric approach
153(2)
5.2.2 Series expansion about the normal distribution
155(4)
5.2.3 Skewed Student t distribution
159(7)
5.2.4 Generating asymmetric distributions
166(3)
5.2.5 Pearson IV distribution
169(3)
5.2.6 Entropy distribution
172(5)
5.3 Specification tests and inference
177(5)
5.3.1 Moment specification tests
177(2)
5.3.2 Adequacy tests based on density forecasts
179(1)
5.3.3 Adequacy tests based on interval forecasts
180(2)
5.4 Illustration
182(6)
5.5 Modeling conditional higher moments
188(7)
5.5.1 Tests for autoregressive conditional higher moments
189(1)
5.5.2 Modeling higher moments directly
189(2)
5.5.3 Modeling the parameters of the distribution
191(4)
6 Modeling Correlation
195(70)
6.1 Multivariate GARCH models
197(26)
6.1.1 Vectorial and diagonal GARCH models
198(2)
6.1.2 Dealing with large-dimensional systems
200(6)
6.1.3 Modeling conditional correlation
206(4)
6.1.4 Estimation issues
210(2)
6.1.5 Specification tests
212(2)
6.1.6 Test of constant conditional correlation matrix
214(3)
6.1.7 Illustration
217(6)
6.2 Modeling the multivariate distribution
223(17)
6.2.1 Standard multivariate distributions
225(5)
6.2.2 Skewed elliptical distribution
230(3)
6.2.3 Skewed Student t distribution
233(3)
6.2.4 Estimation
236(3)
6.2.5 Adequacy tests
239(1)
6.2.6 Illustration
240(1)
6.3 Copula functions
240(25)
6.3.1 Definitions and properties
241(1)
6.3.2 Measures of concordance
242(2)
6.3.3 Non-parametric copulas
244(1)
6.3.4 Review of some copula families
245(9)
6.3.5 Estimation
254(4)
6.3.6 Adequacy tests
258(1)
6.3.7 Modeling the conditional dependency parameter
259(2)
6.3.8 Illustration
261(4)
7 Extreme Value Theory
265(50)
7.1 Univariate tail estimation
266(34)
7.1.1 Distribution of extremes
266(10)
7.1.2 Tail distribution
276(15)
7.1.3 The case of weakly dependent data
291(5)
7.1.4 Estimation of high quantiles
296(4)
7.2 Multivariate dependence
300(15)
7.2.1 Characterizing tail dependency
303(4)
7.2.2 Estimation and statistical inference on X and X
307(1)
7.2.3 Modeling dependency
308(1)
7.2.4 An illustration
309(2)
7.2.5 Further investigations
311(4)
Part III Applications of Non-Gaussian Econometrics
8 Risk Management and VaR
315(34)
8.1 Definitions and measures
316(5)
8.1.1 Definitions
316(4)
8.1.2 Models for portfolio returns
320(1)
8.2 Historical simulation
321(1)
8.3 Semi-parametric approaches
322(8)
8.3.1 Extreme Value Theory (EVT)
324(4)
8.3.2 Quantile regression technique
328(2)
8.4 Parametric approaches
330(11)
8.4.1 RiskMetrics – J.P. Morgan
331(3)
8.4.2 The portfolio-level approach
334(3)
8.4.3 The asset-level approach
337(4)
8.5 Non-linear models
341(1)
8.5.1 The "delta-only" method
341(1)
8.5.2 The "delta-gamma" method
341(1)
8.6 Comparison of VaR models
342(7)
8.6.1 Evaluation of VaR models
343(1)
8.6.2 Comparison of methods
343(1)
8.6.3 10-day VaR and scaling
344(1)
8.6.4 Illustration
345(4)
9 Portfolio Allocation
349(16)
9.1 Portfolio allocation under non-normality
349(10)
9.1.1 Direct maximization of expected utility
350(3)
9.1.2 An approximate solution based on moments
353(6)
9.2 Portfolio allocation under downside risk
359(6)
9.2.1 Definition
360(1)
9.2.2 Downside risk as an additional constraint
360(1)
9.2.3 Downside risk as an optimization criterion
361(4)
Part IV Option Pricing with Non-Gaussian Returns
10 Fundamentals of Option Pricing
365(18)
10.1 Notations
366(3)
10.2 The no-arbitrage approach to option pricing
369(8)
10.2.1 Choice of a stock price process
369(2)
10.2.2 The fundamental partial differential equation
371(2)
10.2.3 Solving the fundamental PDE
373(2)
10.2.4 The Black-Scholes-Merton formula
375(2)
10.3 Martingale measure and BSM formula
377(6)
10.3.1 Self-financing strategies and portfolio construction
377(1)
10.3.2 Change of numeraire
378(1)
10.3.3 Change of Brownian motion
378(1)
10.3.4 Evolution of St under Q
379(1)
10.3.5 The expected pay-off as a martingale
379(1)
10.3.6 The trading strategies
380(1)
10.3.7 Equivalent martingale measure
381(2)
11 Non-structural Option Pricing
383(34)
11.1 Difficulties with the standard BSM model
384(1)
11.2 Direct estimation of the risk-neutral density
385(4)
11.2.1 Expression for the RND
385(2)
11.2.2 Estimating the parameters of the RND
387(2)
11.3 Parametric methods
389(6)
11.3.1 Mixture of log-normal distributions
389(5)
11.3.2 Mixtures of hypergeometric functions
394(1)
11.3.3 Generalized beta distribution
395(1)
11.4 Semi-parametric methods
395(7)
11.4.1 Edgeworth expansions
395(4)
11.4.2 Hermite polynomials
399(3)
11.5 Non-parametric methods
402(7)
11.5.1 Spline methods
402(4)
11.5.2 Tree-based methods
406(1)
11.5.3 Maximum entropy principle
407(1)
11.5.4 Kernel regression
408(1)
11.6 Comparison of various methods
409(5)
11.7 Relationship with real probability
414(3)
11.7.1 The link between RNDs and objective densities
414(2)
11.7.2 Empirical findings
416(1)
12 Structural Option Pricing
417(34)
12.1 Stochastic volatility model
417(8)
12.1.1 The square root process
418(1)
12.1.2 Solving the PDE based on characteristic function
419(3)
12.1.3 A new partial differential equation
422(3)
12.2 Option pricing with stochastic volatility
425(7)
12.2.1 Hull and White (1987, 1988)
425(1)
12.2.2 Heston (1993)
426(2)
12.2.3 Characteristic function of the SV model
428(1)
12.2.4 Further insights
429(3)
12.3 Models with jumps
432(9)
12.3.1 Stochastic process with jumps
432(2)
12.3.2 Diffusion with double exponential jumps
434(2)
12.3.3 Combining stochastic volatility with jumps
436(4)
12.3.4 Jumpy affine models
440(1)
12.4 Models with even wilder jumps: Levy option pricing
441(10)
12.4.1 Commonly used Levy processes
443(1)
12.4.2 Choice of the time-changing process
444(1)
12.4.3 Option pricing
445(1)
12.4.4 Pricing options with risk-neutral characteristic function
446(1)
12.4.5 Empirical results
447(4)
Part V Appendices on Option Pricing Mathematics
13 Brownian Motion and Stochastic Calculus
451(20)
13.1 Law of large numbers and the central limit theorem
451(2)
13.2 Random walks
453(1)
13.3 Construction of the Brownian motion
453(3)
13.4 Properties of the Brownian motion
456(1)
13.5 Stochastic integration
457(2)
13.6 Stochastic differential equations
459(1)
13.7 Ito's lemma
460(2)
13.8 Multivariate extension of Ito's lemma
462(1)
13.9 Transition probabilities and partial differential equations
463(1)
13.10 Kolmogorov backward and forward equations
464(2)
13.11 PDE associated with diffusions
466(2)
13.12 Feynman-Kac formula
468(3)
14 Martingale and Changing Measure
471(6)
14.1 Martingales
471(1)
14.2 Changing probability of a normal distribution
472(1)
14.3 Radon-Nikodym derivative
473(1)
14.4 Girsanov's theorem
474(1)
14.5 Martingale representation theorem
475(2)
15 Characteristic Functions and Fourier Transforms
477(10)
15.1 Characteristic functions
477(6)
15.1.1 Basic properties
478(1)
15.1.2 Moments and the characteristic function
478(1)
15.1.3 Convolution theorem
479(1)
15.1.4 Uniqueness
480(1)
15.1.5 Inversion theorem
480(3)
15.2 Fourier transform and characteristic function
483(4)
16 Jump Processes
487(14)
16.1 Counting and marked point process
487(2)
16.2 The Poisson process
489(5)
16.2.1 Construction of the Poisson distribution
489(2)
16.2.2 Properties of the Poisson distribution
491(1)
16.2.3 Moments of pure Poisson process
492(1)
16.2.4 Compound Poisson process
493(1)
16.3 The exponential distribution
494(3)
16.3.1 Definition and properties
494(1)
16.3.2 Moments of the exponential variable
495(1)
16.3.3 Hazard and survivor functions
496(1)
16.4 Duration between Poisson jumps
497(1)
16.5 Compensated Poisson processes
498(3)
17 Levy Processes
501(6)
17.1 Construction of the Levy process
501(4)
17.2 Properties of Levy processes
505(2)
References 507(28)
Index 535