Financial Statistics and Mathematical Finance : Methods, Models and Applications / Ansgar Steland.
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 sta...
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Full Text (via ProQuest) |
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| Format: | eBook |
| Language: | English |
| Published: |
Hoboken :
John Wiley & Sons,
2012.
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Table of 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.