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Financial Statistics and Mathematical Finance : Methods, Models and Applications.

Author: Ansgar Steland
Publisher: Hoboken : John Wiley & Sons, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Steland, Ansgar.
Financial Statistics and Mathematical Finance : Methods, Models and Applications.
Hoboken : John Wiley & Sons, ©2012
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ansgar Steland
ISBN: 9781118316580 1118316584 9781118316566 1118316568
OCLC Number: 796384801
Description: 1 online resource (433 pages)
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 claims1.4.2 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 preliminaries2.2 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 Stationarity3.3.1 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 measures4.4 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.

Abstract:

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Expl.

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