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

• Autore: Steland Ansgar
• Pubblicazione: Chichester, West Sussex ; ; Hoboken, N.J., : Wiley, 2012
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (433 pages)
• Disciplina: 332.01/5195
• Soggetto topico: Business mathematics; Calculus
• Classificazione: BUS021000
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- 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 -- References -- Index.
• Sommario/riassunto: "The book will focus on elementary financial calculus, statistical models for financial data, option pricing.
• Titolo autorizzato: Financial statistics and mathematical finance
• ISBN: 1-280-77256-5; 9786613683335; 1-118-31654-1; 1-118-31644-4; 1-118-31658-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910814784503321
• Lo trovi qui: Univ. Federico II