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Financial Statistics and Mathematical Finance Methods, Models and Applications

ISBN-10: 0470710586

ISBN-13: 9780470710586

Edition: 2012

Authors: Ansgar Steland

List price: $61.95
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Book details

List price: $61.95
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 7/20/2012
Binding: Hardcover
Pages: 432
Size: 6.75" wide x 9.75" long x 1.00" tall
Weight: 1.738
Language: English

Preface
Acknowledgements
Elementary financial calculus
Motivating examples
Cashflows, interest rates, prices and returns
Bonds and the term structure of interest rates
Asset returns
Some basic models for asset prices
Elementary statistical analysis of returns
Measuring location
Measuring dispersion and risk
Measuring skewness and kurtosis
Estimation of the distribution
Testing for normality
Financial instruments
Contingent claims
Spot contracts and forwards
Futures contracts
Options
Barrier options
Financial engineering
A primer on option pricing
The no-arbitrage principle
Risk-neutral evaluation
Hedging and replication
Nonexistence of a risk-neutral measure
The Black-Scholes pricing formula
The Greeks
Calibration, implied volatility and the smile
Option prices and the risk-neutral density
Notes and further reading
References
Arbitrage theory for the one-period model
Definitions and preliminaries
Linear pricing measures
More on arbitrage
Separation theorems in R<sup>n</sup>
No-arbitrage and martingale measures
Arbitrage-free pricing of contingent claims
Construction of martingale measures: general case
Complete financial markets
Notes and further reading
References
Financial models in discrete time
Adapted stochastic processes in discrete time
Martingales and martingale differences
The martingale transformation
Stopping times, optional sampling and a maximal inequality
Extensions to R<sup>d</sup>
Stationarity
Weak and strict stationarity
Linear processes and ARMA models
Linear processes and the lag operator
Inversion
ARQ(p) and AR(&#8734;) processes
ARMA processes
The frequency domain
The spectrum
The periodogram
Estimation of ARMA processes
(G)ARCH models
Long-memory series
Fractional differences
Fractionally integrated processes
Notes and further reading
References
Arbitrage theory for the multiperiod model
Definitions and preliminaries
Self-financing trading strategies
No-arbitrage and martingale measures
European claims on arbitrage-free markets
The martingale representation theorem in discrete time
The Cox-Ross-Rubinstein binomial model
The Black-Scholes formula
American options and contingent claims
Arbitrage-free pricing and the optimal exercise strategy
Pricing american options using binomial trees
Notes and further reading
References
Brownian motion and related processes in continuous time
Preliminaries
Brownian motion
Definition and basic properties
Brownian motion and the central limit theorem
Path properties
Brownian motion in higher dimensions
Continuity and differentiability
Self-similarity and fractional Brownian motion
Counting processes
The poisson process
The compound poisson process
L�vy processes
Notes and further reading
References
It� Calculus
Total and quadratic variation
Stochastic Stieltjes integration
The It� integral
Quadratic covariation
It�'s formula
It� processes
Diffusion processes and ergodicity
Numerical approximations and statistical estimation
Notes and further reading
References
The Black-Scholes model
The model and first properties
Girsanov's theorem
Equivalent martingale measure
Arbitrage-free pricing and hedging claims
The delta hedge
Time-dependent volatility
The generalized Black-Scholes model
Notes and further reading
References
Limit theory for discrete-time processes
Limit theorems for correlated time series
A regression model for financial time series
Least squares estimation
Limit theorems for martingale difference
Asymptotics
Density estimation and nonparametric regression
Multivariate density estimation
Nonparametric regression
The CLT for linear processes
Mixing processes
Mixing coefficients
Inequalities
Limit theorems for mixing processes
Notes and further reading
References
Special topics
Copulas - and the 2008 financial crisis
Copulas
The financial crisis
Models for credit defaults and CDOs
Local Linear nonparametric regression
Applications in finance: estimation of martingale measures and Ito diffusions
Method and asymptotics
Change-point detection and monitoring
Offline detection
Online detection
Unit roots and random walk
The OLS estimator in the stationary AR(1) model
Nonparametric definitions for the degree of integration
The Dickey-Fuller test
Detecting unit roots and stationarity
Notes and further reading
References
Appendix A
(Stochastic) Landau symbols
Bochner's lemma
Conditional expectation
Inequalities
Random series
Local martingales in discrete time
Weak convergence and central limit theorems
Convergence in distribution
Weak convergence
Prohorov's theorem
Sufficient criteria
More on Skorohod spaces
Central limit theorems for martingale differences
Functional central limit theorems
Strong approximations
References
Index