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Statistics for Finance: Texts in Statistical Science [Minkštas viršelis]

(Lund University, Sweden), (Netcompany, Denmark), (Technical University of Denmark, Lyngby)
  • Formatas: Paperback / softback, 384 pages, aukštis x plotis: 234x156 mm, weight: 710 g
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 18-Dec-2020
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 0367738376
  • ISBN-13: 9780367738372
Kitos knygos pagal šią temą:
Statistics for Finance: Texts in Statistical ScienceDidesnis paveikslėlis
  • Formatas: Paperback / softback, 384 pages, aukštis x plotis: 234x156 mm, weight: 710 g
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 18-Dec-2020
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 0367738376
  • ISBN-13: 9780367738372
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780367738372.html
Raktažodžiai:

Statistics for Finance develops students’ professional skills in statistics with applications in finance. Developed from the authors’ courses at the Technical University of Denmark and Lund University, the text bridges the gap between classical, rigorous treatments of financial mathematics that rarely connect concepts to data and books on econometrics and time series analysis that do not cover specific problems related to option valuation.





The book discusses applications of financial derivatives pertaining to risk assessment and elimination. The authors cover various statistical and mathematical techniques, including linear and nonlinear time series analysis, stochastic calculus models, stochastic differential equations, Ito’s formula, the Black–Scholes model, the generalized method-of-moments, and the Kalman filter. They explain how these tools are used to price financial derivatives, identify interest rate models, value bonds, estimate parameters, and much more.





This textbook will help students understand and manage empirical research in financial engineering. It includes examples of how the statistical tools can be used to improve value-at-risk calculations and other issues. In addition, end-of-chapter exercises develop students’ financial reasoning skills.

Preface xv
Author biographies xvii
1 Introduction
1(16)
1.1 Introduction to financial derivatives
2(4)
1.2 Financial derivatives --- what's the big deal?
6(3)
1.3 Stylized facts
9(5)
1.3.1 No autocorrelation in returns
10(1)
1.3.2 Unconditional heavy tails
10(1)
1.3.3 Gain/loss asymmetry
10(1)
1.3.4 Aggregational Gaussianity
11(1)
1.3.5 Volatility clustering
12(1)
1.3.6 Conditional heavy tails
12(1)
1.3.7 Significant autocorrelation for absolute returns
12(1)
1.3.8 Leverage effects
13(1)
1.4 Overview
14(3)
2 Fundamentals
17(20)
2.1 Interest rates
18(3)
2.1.1 Future and present value of a single payment
18(1)
2.1.2 Annuities
19(1)
2.1.3 Future value of an annuity
19(1)
2.1.4 Present value of a unit annuity
20(1)
2.2 Cash flows
21(4)
2.3 Continuously compounded interest rates
25(2)
2.4 Interest rate options: caps and floors
27(5)
2.5 Notes
32(1)
2.6 Problems
32(5)
3 Discrete time finance
37(20)
3.1 The binomial one-period model
37(2)
3.2 One-period model
39(5)
3.2.1 Risk-neutral probabilities
40(1)
3.2.2 Complete and incomplete markets
41(3)
3.3 Multiperiod model
44(9)
3.3.1 σ-algebras and information sets
47(2)
3.3.2 Financial multiperiod markets
49(1)
3.3.3 Martingale measures
50(3)
3.4 Notes
53(1)
3.5 Problems
53(4)
4 Linear time series models
57(16)
4.1 Introduction
57(2)
4.2 Linear systems in the time domain
59(3)
4.3 Linear stochastic processes
62(1)
4.4 Linear processes with a rational transfer function
63(3)
4.4.1 ARMA process
63(1)
4.4.2 ARIMA process
64(1)
4.4.3 Seasonal models
65(1)
4.5 Autocovariance functions
66(1)
4.5.1 Autocovariance function for ARMA processes
66(1)
4.6 Prediction in linear processes
67(2)
4.7 Problems
69(4)
5 Nonlinear time series models
73(30)
5.1 Introduction
73(1)
5.2 Aim of model building
73(1)
5.3 Qualitative properties of the models
74(3)
5.3.1 Volterra series expansion
74(1)
5.3.2 Generalized transfer functions
75(2)
5.4 Parameter estimation
77(5)
5.4.1 Maximum likelihood estimation
77(1)
5.4.1.1 Cramer--Rao bound
78(1)
5.4.1.2 The likelihood ratio test
79(1)
5.4.2 Quasi-maximum likelihood
79(1)
5.4.3 Generalized method of moments
80(1)
5.4.3.1 GMM and moment restrictions
80(1)
5.4.3.2 Standard error of the estimates
81(1)
5.4.3.3 Estimation of the weight matrix
81(1)
5.4.3.4 Nested tests for model reduction
82(1)
5.5 Parametric models
82(16)
5.5.1 Threshold and regime models
84(1)
5.5.1.1 Self-exciting threshold AR (SETAR)
84(2)
5.5.1.2 Self-exciting threshold ARMA (SETARMA)
86(1)
5.5.1.3 Open loop threshold AR (TARSO)
86(1)
5.5.1.4 Smooth threshold AR (STAR)
86(1)
5.5.1.5 Hidden Markov models and related models
87(2)
5.5.2 Models with conditional heteroscedasticity (ARCH)
89(1)
5.5.2.1 ARCH regression model
89(1)
5.5.2.2 GARCH model
90(1)
5.5.2.3 EGARCH model
91(1)
5.5.2.4 FIGARCH model
92(1)
5.5.2.5 ARCH-M model
92(1)
5.5.2.6 SW-ARCH model
93(1)
5.5.2.7 General remarks on ARCH models
93(2)
5.5.2.8 Multivariate GARCH models
95(1)
5.5.3 Stochastic volatility models
96(2)
5.6 Model identification
98(1)
5.7 Prediction in nonlinear models
98(1)
5.8 Applications of nonlinear models
99(2)
5.8.1 Electricity spot prices
99(1)
5.8.2 Comparing ARCH models
100(1)
5.9 Problems
101(2)
6 Kernel estimators in time series analysis
103(14)
6.1 Non-parametric estimation
103(1)
6.2 Kernel estimators for time series
103(3)
6.2.1 Introduction
103(1)
6.2.2 Kernel estimator
104(1)
6.2.3 Central limit theorems
105(1)
6.3 Kernel estimation for regression
106(4)
6.3.1 Estimator for regression
106(1)
6.3.2 Product kernel
107(1)
6.3.3 Non-parametric estimation of the pdf
108(1)
6.3.4 Non-parametric LS
108(1)
6.3.5 Bandwidth
108(1)
6.3.6 Selection of bandwidth --- cross validation
109(1)
6.3.7 Variance of the non-parametric estimates
109(1)
6.4 Applications of kernel estimators
110(6)
6.4.1 Non-parametric estimation of the conditional mean and variance
110(1)
6.4.2 Non-parametric estimation of non-stationarity --- an example
111(2)
6.4.3 Non-parametric estimation of dependence on external variables --- an example
113(1)
6.4.4 Non-parametric GARCH models
114(2)
6.5 Notes
116(1)
7 Stochastic calculus
117(22)
7.1 Dynamical systems
118(2)
7.2 The Wiener process
120(2)
7.3 Stochastic Integrals
122(3)
7.4 Ito stochastic calculus
125(5)
7.5 Extensions to jump processes
130(6)
7.6 Problems
136(3)
8 Stochastic differential equations
139(36)
8.1 Stochastic Differential Equations
140(12)
8.1.1 Existence and uniqueness
142(5)
8.1.2 Ito formula
147(2)
8.1.3 Multivariate SDEs
149(2)
8.1.4 Stratonovitch SDE
151(1)
8.2 Analytical solution methods
152(4)
8.2.1 Linear, univariate SDEs
152(4)
8.3 Feynman--Kac representation
156(3)
8.4 Girsanov measure transformation
159(12)
8.4.1 Measure theory
159(2)
8.4.2 Radon--Nikodym theorem
161(3)
8.4.3 Girsanov transformation
164(4)
8.4.4 Maximum likelihood estimation for continuously observed diffusions
168(3)
8.5 Notes
171(1)
8.6 Problems
172(3)
9 Continuous-time security markets
175(20)
9.1 From discrete to continuous time
175(2)
9.2 Classical arbitrage theory
177(8)
9.2.1 Black--Scholes formula
181(2)
9.2.2 Hedging strategies
183(1)
9.2.2.1 Quadratic hedging
184(1)
9.3 Modern approach using martingale measures
185(4)
9.4 Pricing
189(1)
9.5 Model extensions
190(1)
9.6 Computational methods
191(2)
9.6.1 Fourier methods
192(1)
9.7 Problems
193(2)
10 Stochastic interest rate models
195(14)
10.1 Gaussian one-factor models
196(2)
10.1.1 Merton model
196(1)
10.1.2 Vasicek model
197(1)
10.2 A general class of one-factor models
198(3)
10.3 Time-dependent models
201(1)
10.3.1 Ho--Lee
201(1)
10.3.2 Black--Derman--Toy
201(1)
10.3.3 Hull--White
201(1)
10.3.3.1 CIR++ model
202(1)
10.4 Multifactor and stochastic volatility models
202(4)
10.4.1 Stochastic volatility models
204(1)
10.4.2 Affine Term Structure models
205(1)
10.5 Notes
206(1)
10.6 Problems
206(3)
11 Term structure of interest rates
209(44)
11.1 Basic concepts
210(11)
11.1.1 Known interest rates
210(2)
11.1.2 Discrete dividends
212(2)
11.1.3 Yield curve
214(3)
11.1.4 Stochastic interest rates
217(4)
11.2 Classical approach
221(11)
11.2.1 Exogenous specification of the market price of risk
227(1)
11.2.2 Illustrative example
228(3)
11.2.3 Modern approach
231(1)
11.3 Term structure for specific models
232(8)
11.3.1 Example 1: The Vasicek model
235(2)
11.3.2 Example 2: The Ho--Lee model
237(1)
11.3.3 Example 3: The Cox--Ingersoll--Ross model
238(1)
11.3.4 Multifactor models
239(1)
11.4 Heath--Jarrow--Morton framework
240(5)
11.5 Credit models
245(1)
11.5.1 Intensity models
245(1)
11.6 Estimation of the term structure --- curve-fitting
246(3)
11.6.1 Polynomial methods
247(1)
11.6.2 Decay functions
247(1)
11.6.3 Nelson--Siegel method
247(2)
11.7 Notes
249(1)
11.8 Problems
250(3)
12 Discrete time approximations
253(12)
12.1 Stochastic Taylor expansion
253(1)
12.2 Convergence
254(1)
12.3 Discretization schemes
255(3)
12.3.1 Strong Taylor approximations
255(1)
12.3.1.1 Explicit Euler scheme
255(1)
12.3.1.2 Milstein scheme
256(1)
12.3.1.3 The order 1.5 strong Taylor scheme
256(1)
12.3.2 Weak Taylor approximations
257(1)
12.3.2.1 The order 2.0 weak Taylor scheme
257(1)
12.3.3 Exponential approximation
257(1)
12.4 Multilevel Monte Carlo
258(1)
12.5 Simulation of SDEs
259(6)
13 Parameter estimation in discretely observed SDEs
265(18)
13.1 Introduction
265(1)
13.2 High frequency methods
266(3)
13.3 Approximate methods for linear and non-linear models
269(1)
13.4 State dependent diffusion term
269(2)
13.4.1 A transformation approach
269(2)
13.5 MLE for non-linear diffusions
271(3)
13.5.1 Simulation-based estimators
271(1)
13.5.1.1 Jump diffusions
272(1)
13.5.2 Numerical methods for the Fokker--Planck equation
273(1)
13.5.3 Series expansion
273(1)
13.6 Generalized method of moments
274(3)
13.6.1 GMM and moment restrictions
275(2)
13.7 Model validation for discretely observed SDEs
277(3)
13.7.1 Generalized Gaussian residuals
277(1)
13.7.1.1 Case study
278(2)
13.8 Problems
280(3)
14 Inference in partially observed processes
283(40)
14.1 Introduction
283(1)
14.2 Model
284(1)
14.3 Exact filtering
285(3)
14.3.1 Prediction
285(1)
14.3.1.1 Scalar case
285(1)
14.3.1.2 General case
286(1)
14.3.2 Updating
287(1)
14.4 Conditional moment estimators
288(1)
14.4.1 Prediction and updating
288(1)
14.5 Kalman filter
289(1)
14.6 Approximate filters
290(6)
14.6.1 Truncated second order filter
290(1)
14.6.2 Linearized Kalman filter
291(1)
14.6.3 Extended Kalman filter
291(2)
14.6.4 Statistically linearized filter
293(1)
14.6.5 Non-linear models
294(1)
14.6.6 Linear time-varying models
295(1)
14.6.7 Linear time-invariant models
295(1)
14.6.8 Case: Affine term structure models
296(1)
14.7 State filtering and prediction
296(4)
14.7.1 Linear models
297(1)
14.7.1.1 Linear time-varying models
297(1)
14.7.1.2 Linear time-invariant models
297(1)
14.7.2 The system equation in discrete time
298(1)
14.7.3 Non-linear models
299(1)
14.8 Unscented Kalman Filter
300(2)
14.9 A maximum likelihood method
302(3)
14.10 Sequential Monte Carlo filters
305(5)
14.10.1 Optimal filtering
306(1)
14.10.2 Bootstrap filter
307(2)
14.10.3 Parameter estimation
309(1)
14.11 Application of non-linear filters
310(11)
14.11.1 Sequential calibration of options
310(4)
14.11.2 Computing Value at Risk in a stochastic volatility model
314(1)
14.11.3 Extended Kalman filtering applied to bonds
315(3)
14.11.4 Case 1: A Wiener process
318(1)
14.11.5 Case 2: The Vasicek model
319(2)
14.12 Problems
321(2)
A Projections in Hilbert spaces
323(14)
A.1 Introduction
323(1)
A.2 Hilbert spaces
324(1)
A.3 The projection theorem
325(4)
A.3.1 Prediction equations
328(1)
A.4 Conditional expectation and linear projections
329(3)
A.5 Kalman filter
332(2)
A.6 Projections in Rn
334(3)
B Probability theory
337(8)
B.1 Measures and σ-algebras
337(1)
B.2 Partitions and information
338(1)
B.3 Conditional expectation
339(4)
B.4 Notes
343(2)
Bibliography 345(16)
Index 361
Erik Lindström is an associate professor in the Centre for Mathematical Sciences at Lund University. His research ranges from statistical methodology (primarily time series analysis in discrete and continuous time) to financial mathematics as well as problems related to energy markets. He earned a PhD in mathematical statistics from Lund Institute of Technology/Lund University.





Henrik Madsen is a professor and head of the Section for Dynamical Systems in the Department for Applied Mathematics and Computer Sciences at the Technical University of Denmark. An elected member of the ISI and IEEE, he has authored or co-authored 480 papers and 11 books in areas including mathematical statistics, time series analysis, and the integration of renewables in electricity markets. He earned a PhD in statistics from the Technical University of Denmark.





Jan Nygaard Nielsen is a principal architect at Netcompany, a Danish IT and business consulting firm. He earned a PhD from the Technical University of Denmark.