Financial statistics and mathematical finance: methods, models and applications

INDICE: Preface 71 Elementary Financial Calculus 11.1 Motivating Examples 11.2 Cashflows, interest rates, prices and returns 21.2.1 Bonds and the term structure of interest rates 51.2.2 Asset returns 61.2.3 Some basic models for asset prices 71.3 Elementary statistical analysis of returns 111.3.1 Measuring location 131.3.2 Measuring dispersion and risk 151.3.3 Measuring skewness and kurtosis 191.3.4 Estimation of the distribution 201.3.5 Testing for normality 261.4 Financial instruments 281.4.1 Contingent claims 281.4.2 Spot contracts and forwards 281.4.3 Futures contracts 291.4.4 Options 291.4.5 Barrier Options 301.4.6 Financial engineering 311.5 A Primer on Option Pricing 321.5.1 The no-arbitrage principle 321.5.2 Risk-neutral evaluation 331.5.3 Hedging and replication 351.5.4 Non-existence of a risk-neutral measure 361.5.5 The Black-Scholespricing formula 361.5.6 The Greeks 381.5.7 Calibration, implied volatility and the smile 401.5.8 Option prices and the risk-neutral density 411.6 Notes andfurther reading 42References 432 Arbitrage Theory for the One-Period Model 452.1 Definitions and preliminaries 452.2 Linear pricing measures 472.3 More on arbitrage 502.4 Separation theorems in Rn 522.5 No-arbitrage and martingale measures 552.6 Arbitrage-free pricing of contingent claims 632.7 Construction ofMartingaleMeasures: General Case 682.8 Complete financial markets 712.9 Notesand further reading 74References 743 Financial Models in Discrete Time 753.1 Adapted stochastic processes in discrete time 773.2 Martingales and martingaledifferences 813.2.1 The martingale transformation 873.2.2 Stopping times, optional sampling and a maximal inequality 883.2.3 Extensions to Rd 973.3 Stationarity 973.3.1 Weak and strict stationarity 983.4 Linear Processes and ARMA Models 1063.4.1 Linear processes and the lag operator 1063.4.2 Inversion 1113.4.3AR(p) and AR(?) processes 1133.4.4 ARMA processes 1173.5 The frequency domain1183.5.1 The spectrum 1183.5.2 The periodogram 1213.6 Estimation of ARMA processes 1263.7 (G)ARCH models 1273.8 Long memory series 1333.8.1 Fractional differences 1333.8.2 Fractionally integrated processes 1373.9 Notes and further reading 137References 1384 Arbitrage Theory for the Multi-Period Model 1394.1 Definitions and preliminaries 1394.2 Self-financing trading strategies 1404.3 No-arbitrage and martingale measures 1434.4 European claims on arbitrage-free markets 1464.5 The martingale representation theorem in discrete time 1504.6 TheCox-Ross-Rubinstein binomial model 1514.7 The Black-Scholes formula 1564.8 American options and contingent claims 1614.8.1 Arbitrage-free pricing and the optimal exercise strategy 1614.8.2 Pricing American options using binomial trees 1644.9 Notes and further reading 165References 1665 Brownian Motion and Related Processes in Continuous Time 1675.1 Preliminaries 1675.2 Brownian Motion 1705.2.1 Definition and basic properties 1705.2.2 Brownian motion and the central limit theorem 1775.2.3 Path properties 1795.2.4 Brownian motion in higher dimensions 1805.3 Continuity and differentiability 1815.4 Self-similarity and fractional Brownian motion 1835.5 Counting processes 1845.5.1 The Poisson process 1845.5.2 The compound Poisson process 1865.6 L´evy processes 1885.7 Notes and further reading 190References 1906 Itˆo Calculus 1916.1 Total and quadraticvariation 1916.2 Stochastic Stieltjes integration 1966.3 The Itˆo integral 1996.4 Quadratic covariation 2116.5 Itˆo’s formula 2126.6 Itˆo processes 2156.7 Diffusion processes and ergodicity 2226.8 Numerical approximations and statistical estimation 2236.9 Notes and further reading 225References 2257 The Black-Scholes-Model 2277.1 The model and first properties 2277.2 Girsanov’s theorem 2337.3 Equivalent martingale measure 2377.4 Arbitrage-free pricing and hedgingclaims 2387.5 The delta hedge 2417.6 Time-dependent volatility 2427.7 The generalized Black-Scholes model 2447.8 Notes and further reading 246References 2468 Limit Theory for Discrete-Time Processes 2498.1 Limit theorems for correlated time series 2508.2 A regression model for financial time series 2598.2.1 Least squares estimation 2618.3 Limit theorems for martingale difference 2638.4 Asymptotics 2688.5 Density estimation and nonparametric regression 2728.5.1 Multivariate density estimation 2728.5.2 Nonparametric regression 2808.6 The CLTfor linear processes 2878.7 Mixing Processes 2908.7.1 Mixing coefficients 2908.7.2 Inequalities 2928.8 Limit Theorems for Mixing Processes 2978.9 Notes andfurther reading 306References 3069 Special Topics 3099.1 Copulas - and the 2008 financial crisis 3099.1.1 Copulas 3109.1.2 The financial crisis 3169.1.3 Models for credit defaults and CDOs 3199.2 Local linear nonparametric regression3229.2.1 Applications in finance: Estimation of martingale measures and Itˆodiffusions 3229.2.2 Method and asymptotics 3249.3 Change-point detection and monitoring 3339.3.1 Offline detection 3349.3.2 Online detection 3429.4 Unit roots and random walk 3459.4.1 The OLS estimator in the stationary AR(1) model 3479.4.2 Nonparametric definitions for the degree of integration 3519.4.3 The Dickey-Fuller test 3529.4.4 Detecting unit roots and stationarity 3559.5 Notes and further reading 363References 363A Appendix A 365A.1 (Stochastic) Landau Symbols 365A.2 Bochner’s Lemma 366A.3 Conditional Expectation 367A.4 Inequalities368A.5 Random Series 369A.6 Local martingales in discrete time 369Appendix B Weak Convergence and Central Limit Theorems 371B.1 Convergence in distribution371B.2 Weak convergence 372B.3 Prohorov’s theorem 377B.4 Sufficient criteria 379B.5 More on Skorohod spaces 381B.6 Central Limit Theorems for Martingale Differences 381B.7 Functional central limit theorems 382B.8 Strong Approximations 384References 386Index

• ISBN: 978-0-470-71058-6
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 400
• Fecha Publicación: 29/06/2012
• Nº Volúmenes: 1
• Idioma: Inglés