Financial statistics and mathematical finance : methods, models and applications / Ansgar Steland.

Format:

Book

Author/Creator:

Steland, Ansgar.

Language:

English

Subjects (All):

Business mathematics.

Calculus.

Physical Description:

1 online resource (433 pages)

Edition:

1st ed.

Place of Publication:

Chichester, West Sussex ; Hoboken, N.J. : Wiley, 2012.

Language Note:

English

Summary:

"The book will focus on elementary financial calculus, statistical models for financial data, option pricing.

Contents:

Financial Statistics and Mathematical Finance: Methods, Models and Applications

Contents

Preface

Acknowledgements

1 Elementary financial calculus

1.1 Motivating examples

1.2 Cashflows, interest rates, prices and returns

1.2.1 Bonds and the term structure of interest rates

1.2.2 Asset returns

1.2.3 Some basic models for asset prices

1.3 Elementary statistical analysis of returns

1.3.1 Measuring location

1.3.2 Measuring dispersion and risk

1.3.3 Measuring skewness and kurtosis

1.3.4 Estimation of the distribution

1.3.5 Testing for normality

1.4 Financial instruments

1.4.1 Contingent claims

1.4.2 Spot contracts and forwards

1.4.3 Futures contracts

1.4.4 Options

1.4.5 Barrier options

1.4.6 Financial engineering

1.5 A primer on option pricing

1.5.1 The no-arbitrage principle

1.5.2 Risk-neutral evaluation

1.5.3 Hedging and replication

1.5.4 Nonexistence of a risk-neutral measure

1.5.5 The Black-Scholes pricing formula

1.5.6 The Greeks

1.5.7 Calibration, implied volatility and the smile

1.5.8 Option prices and the risk-neutral density

1.6 Notes and further reading

References

2 Arbitrage theory for the one-period model

2.1 Definitions and preliminaries

2.2 Linear pricing measures

2.3 More on arbitrage

2.4 Separation theorems in Rn

2.5 No-arbitrage and martingale measures

2.6 Arbitrage-free pricing of contingent claims

2.7 Construction of martingale measures: general case

2.8 Complete financial markets

2.9 Notes and further reading

3 Financial models in discrete time

3.1 Adapted stochastic processes in discrete time

3.2 Martingales and martingale differences

3.2.1 The martingale transformation

3.2.2 Stopping times, optional sampling and a maximal inequality

3.2.3 Extensions to Rd.

3.3 Stationarity

3.3.1 Weak and strict stationarity

3.4 Linear processes and ARMA models

3.4.1 Linear processes and the lag operator

3.4.2 Inversion

3.4.3 AR(p) and AR(∞) processes

3.4.4 ARMA processes

3.5 The frequency domain

3.5.1 The spectrum

3.5.2 The periodogram

3.6 Estimation of ARMA processes

3.7 (G)ARCH models

3.8 Long-memory series

3.8.1 Fractional differences

3.8.2 Fractionally integrated processes

3.9 Notes and further reading

4 Arbitrage theory for the multiperiod model

4.1 Definitions and preliminaries

4.2 Self-financing trading strategies

4.3 No-arbitrage and martingale measures

4.4 European claims on arbitrage-free markets

4.5 The martingale representation theorem in discrete time

4.6 The Cox-Ross-Rubinstein binomial model

4.7 The Black-Scholes formula

4.8 American options and contingent claims

4.8.1 Arbitrage-free pricing and the optimal exercise strategy

4.8.2 Pricing american options using binomial trees

4.9 Notes and further reading

5 Brownian motion and related processes in continuous time

5.1 Preliminaries

5.2 Brownian motion

5.2.1 Definition and basic properties

5.2.2 Brownian motion and the central limit theorem

5.2.3 Path properties

5.2.4 Brownian motion in higher dimensions

5.3 Continuity and differentiability

5.4 Self-similarity and fractional Brownian motion

5.5 Counting processes

5.5.1 The poisson process

5.5.2 The compound poisson process

5.6 Lévy processes

5.7 Notes and further reading

6 Itô Calculus

6.1 Total and quadratic variation

6.2 Stochastic Stieltjes integration

6.3 The Itô integral

6.4 Quadratic covariation

6.5 Itô's formula

6.6 Itô processes

6.7 Diffusion processes and ergodicity.

6.8 Numerical approximations and statistical estimation

6.9 Notes and further reading

7 The Black-Scholes model

7.1 The model and first properties

7.2 Girsanov's theorem

7.3 Equivalent martingale measure

7.4 Arbitrage-free pricing and hedging claims

7.5 The delta hedge

7.6 Time-dependent volatility

7.7 The generalized Black-Scholes model

7.8 Notes and further reading

8 Limit theory for discrete-time processes

8.1 Limit theorems for correlated time series

8.2 A regression model for financial time series

8.2.1 Least squares estimation

8.3 Limit theorems for martingale difference

8.4 Asymptotics

8.5 Density estimation and nonparametric regression

8.5.1 Multivariate density estimation

8.5.2 Nonparametric regression

8.6 The CLT for linear processes

8.7 Mixing processes

8.7.1 Mixing coefficients

8.7.2 Inequalities

8.8 Limit theorems for mixing processes

8.9 Notes and further reading

9 Special topics

9.1 Copulas - and the 2008 financial crisis

9.1.1 Copulas

9.1.2 The financial crisis

9.1.3 Models for credit defaults and CDOs

9.2 Local Linear nonparametric regression

9.2.1 Applications in finance: estimation of martingale measures and Itô diffusions

9.2.2 Method and asymptotics

9.3 Change-point detection and monitoring

9.3.1 Offline detection

9.3.2 Online detection

9.4 Unit roots and random walk

9.4.1 The OLS estimator in the stationary AR(1) model

9.4.2 Nonparametric definitions for the degree of integration

9.4.3 The Dickey-Fuller test

9.4.4 Detecting unit roots and stationarity

9.5 Notes and further reading

Appendix A

A.1 (Stochastic) Landau symbols

A.2 Bochner's lemma

A.3 Conditional expectation

A.4 Inequalities

A.5 Random series.

A.6 Local martingales in discrete time

Appendix B: Weak convergence and central limit theorems

B.1 Convergence in distribution

B.2 Weak convergence

B.3 Prohorov's theorem

B.4 Sufficient criteria

B.5 More on Skorohod spaces

B.6 Central limit theorems for martingale differences

B.7 Functional central limit theorems

B.8 Strong approximations

Index.

Notes:

Includes bibliographical references and index.

ISBN:

9786613683335

9781280772566

1280772565

9781118316542

1118316541

9781118316443

1118316444

9781118316580

1118316584

OCLC:

796384801