| Description |
1 online resource (885 pages) |
| Contents |
880-01 Front Matter -- A Synthetic View -- Probability, Random Variables and Statistics -- Stochastic Processes -- Numerical Methods -- Estimation of Stochastic Models for Finance -- European Option Pricing -- American Options -- Pricing Outside the Standard Black and Scholes Model -- Miscellanea -- Appendix A: ₁How to₂ Guide to R -- Appendix B: R in Finance -- Index |
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880-01/(S Machine generated contents note: 1. synthetic view -- 1.1. world of derivatives -- 1.1.1. Different kinds of contracts -- 1.1.2. Vanilla options -- 1.1.3. Why options-- 1.1.4. variety of options -- 1.1.5. How to model asset prices -- 1.1.6. One step beyond -- 1.2. Bibliographical notes -- References -- 2. Probability, random variables and statistics -- 2.1. Probability -- 2.1.1. Conditional probability -- 2.2. Bayes' rule -- 2.3. Random variables -- 2.3.1. Characteristic function -- 2.3.2. Moment generating function -- 2.3.3. Examples of random variables -- 2.3.4. Sum of random variables -- 2.3.5. Infinitely divisible distributions -- 2.3.6. Stable laws -- 2.3.7. Fast Fourier Transform -- 2.3.8. Inequalities -- 2.4. Asymptotics -- 2.4.1. Types of convergences -- 2.4.2. Law of large numbers -- 2.4.3. Central limit theorem -- 2.5. Conditional expectation -- 2.6. Statistics -- 2.6.1. Properties of estimators -- 2.6.2. likelihood function -- 2.6.3. Efficiency of estimators -- 2.6.4. Maximum likelihood estimation -- 2.6.5. Moment type estimators -- 2.6.6. Least squares method -- 2.6.7. Estimating functions -- 2.6.8. Confidence intervals -- 2.6.9. Numerical maximization of the likelihood -- 2.6.10. δ-method -- 2.7. Solution to exercises -- 2.8. Bibliographical notes -- References -- 3. Stochastic processes -- 3.1. Definition and first properties -- 3.1.1. Measurability and filtrations -- 3.1.2. Simple and quadratic variation of a process -- 3.1.3. Moments, covariance, and increments of stochastic processes -- 3.2. Martingales -- 3.2.1. Examples of martingales -- 3.2.2. Inequalities for martingales -- 3.3. Stopping times -- 3.4. Markov property -- 3.4.1. Discrete time Markov chains -- 3.4.2. Continuous time Markov processes -- 3.4.3. Continuous time Markov chains -- 3.5. Mixing property -- 3.6. Stable convergence -- 3.7. Brownian motion -- 3.7.1. Brownian motion and random walks -- 3.7.2. Brownian motion is a martingale -- 3.7.3. Brownian motion and partial differential equations -- 3.8. Counting and marked processes -- 3.9. Poisson process -- 3.10. Compound Poisson process -- 3.11. Compensated Poisson processes -- 3.12. Telegraph process -- 3.12.1. Telegraph process and partial differential equations -- 3.12.2. Moments of the telegraph process -- 3.12.3. Telegraph process and Brownian motion -- 3.13. Stochastic integrals -- 3.13.1. Properties of the stochastic integral -- 3.13.2. Ito formula -- 3.14. More properties and inequalities for the Ito integral -- 3.15. Stochastic differential equations -- 3.15.1. Existence and uniqueness of solutions -- 3.16. Girsanov's theorem for diffusion processes -- 3.17. Local martingales and semimartingales -- 3.18. Levy processes -- 3.18.1. Levy-Khintchine formula -- 3.18.2. Levy jumps and random measures -- 3.18.3. Ito-Levy decomposition of a Levy process -- 3.18.4. More on the Levy measure -- 3.18.5. Ito formula for Levy processes -- 3.18.6. Levy processes and martingales -- 3.18.7. Stochastic differential equations with jumps -- 3.18.8. Ito formula for Levy driven stochastic differential equations -- 3.19. Stochastic differential equations in Rn -- 3.20. Markov switching diffusions -- 3.21. Solution to exercises -- 3.22. Bibliographical notes -- References -- 4. Numerical methods -- 4.1. Monte Carlo method -- 4.1.1. application -- 4.2. Numerical differentiation -- 4.3. Root finding -- 4.4. Numerical optimization -- 4.5. Simulation of stochastic processes -- 4.5.1. Poisson processes -- 4.5.2. Telegraph process -- 4.5.3. One-dimensional diffusion processes -- 4.5.4. Multidimensional diffusion processes -- 4.5.5. Levy processes -- 4.5.6. Simulation of stochastic differential equations with jumps -- 4.5.7. Simulation of Markov switching diffusion processes -- 4.6. Solution to exercises -- 4.7. Bibliographical notes -- References -- 5. Estimation of stochastic models for finance -- 5.1. Geometric Brownian motion -- 5.1.1. Properties of the increments -- 5.1.2. Estimation of the parameters -- 5.2. Quasi-maximum likelihood estimation -- 5.3. Short-term interest rates models -- 5.3.1. special case of the CIR model -- 5.3.2. Ahn-Gao model -- 5.3.3. Ait-Sahalia model -- 5.4. Exponential Levy model -- 5.4.1. Examples of Levy models in finance -- 5.5. Telegraph and geometric telegraph process -- 5.5.1. Filtering of the geometric telegraph process -- 5.6. Solution to exercises -- 5.7. Bibliographical notes -- References -- 6. European option pricing -- 6.1. Contingent claims -- 6.1.1. main ingredients of option pricing -- 6.1.2. One period market -- 6.1.3. Black and Scholes market -- 6.1.4. Portfolio strategies -- 6.1.5. Arbitrage and completeness -- 6.1.6. Derivation of the Black and Scholes equation -- 6.2. Solution of the Black and Scholes equation -- 6.2.1. European call and put prices -- 6.2.2. Put-call parity -- 6.2.3. Option pricing with R -- 6.2.4. Monte Carlo approach -- 6.2.5. Sensitivity of price to parameters -- 6.3. δ-hedging and the Greeks -- 6.3.1. hedge ratio as a function of time -- 6.3.2. Hedging of generic options -- 6.3.3. density method -- 6.3.4. numerical approximation -- 6.3.5. Monte Carlo approach -- 6.3.6. Mixing Monte Carlo and numerical approximation -- 6.3.7. Other Greeks of options -- 6.3.8. Put and call Greeks with Rmetrics -- 6.4. Pricing under the equivalent martingale measure -- 6.4.1. Pricing of generic claims under the risk neutral measure -- 6.4.2. Arbitrage and equivalent martingale measure -- 6.5. More on numerical option pricing -- 6.5.1. Pricing of path-dependent options -- 6.5.2. Asian option pricing via asymptotic expansion -- 6.5.3. Exotic option pricing with Rmetrics -- 6.6. Implied volatility and volatility smiles -- 6.6.1. Volatility smiles -- 6.7. Pricing of basket options -- 6.7.1. Numerical implementation -- 6.7.2. Completeness and arbitrage -- 6.7.3. example with two assets -- 6.7.4. Numerical pricing -- 6.8. Solution to exercises -- 6.9. Bibliographical notes -- References -- 7. American options -- 7.1. Finite difference methods -- 7.2. Explicit finite-difference method -- 7.2.1. Numerical stability -- 7.3. Implicit finite-difference method -- 7.4. quadratic approximation -- 7.5. Geske and Johnson and other approximations -- 7.6. Monte Carlo methods -- 7.6.1. Broadie and Glasserman simulation method -- 7.6.2. Longstaff and Schwartz Least Squares Method -- 7.7. Bibliographical notes -- References -- 8. Pricing outside the standard Black and Scholes model -- 8.1. Levy market model -- 8.1.1. Why the Levy market is incomplete-- 8.1.2. Esscher transform -- 8.1.3. mean-correcting martingale measure -- 8.1.4. Pricing of European options -- 8.1.5. Option pricing using Fast Fourier Transform method -- 8.1.6. numerical implementation of the FFT pricing -- 8.2. Pricing under the jump telegraph process -- 8.3. Markov switching diffusions -- 8.3.1. Monte Carlo pricing -- 8.3.2. Semi-Monte Carlo method -- 8.3.3. Pricing with the Fast Fourier Transform -- 8.3.4. Other applications of Markov switching diffusion models -- 8.4. benchmark approach -- 8.4.1. Benchmarking of the savings account -- 8.4.2. Benchmarking of the risky asset -- 8.4.3. Benchmarking the option price -- 8.4.4. Martingale representation of the option price process -- 8.5. Bibliographical notes -- References -- 9. Miscellanea -- 9.1. Monitoring of the volatility -- 9.1.1. least squares approach -- 9.1.2. Analysis of multiple change points -- 9.1.3. example of real-time analysis -- 9.1.4. More general quasi maximum likelihood approach -- 9.1.5. Construction of the quasi-MLE -- 9.1.6. modified |
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Machine generated contents note: Preface -- 1. A Synthetic View -- 1.1 The World of Derivatives -- 1.2 Bibliographic Notes -- References -- 2. Probability, Random Variables and Statistics -- 2.1 Probability -- 2.2 Bayes' Rule -- 2.3 Random Variables -- 2.4 Asymptotics -- 2.5 Conditional Expectation -- 2.6 Statistics -- 2.7 Solution to Exercises -- 2.8 Bibliographic Notes -- References -- 3. Stochastic Processes -- 3.1 Definition and First Properties -- 3.3 Stopping Times -- 3.4 Markov Property -- 3.5 Mixing Property -- 3.6 Stable Convergence -- 3.7 Brownian Motion -- 3.8 Counting and Marked Processes -- 3.9 Poisson Process -- 3.10 Compound Poisson process -- 3.11 Compensated Poisson processes -- 3.12 Telegraph Process -- 3.13 Stochastic Integrals -- 3.14 More Properties and Inequalities for the Itô Integral -- 3.15 Stochastic Differential Equations -- 3.16 Girsanov's theorem for diffusion processes -- 3.17 Local Martingales and Semimartingales -- 3.18 Levy Processes -- 3.19 Stochastic Differential Equations in Rn -- 3.20 Markov Switching Diffusions -- 3.21 Solution to Exercises -- 3.22 Bibliographic Notes -- References -- 4. Numerical Methods -- 4.1 Monte Carlo Method -- 4.2 Numerical Differentiation -- 4.3 Root Finding -- 4.4 Numerical Optimization -- 4.5 Simulation of Stochastic Processes -- 4.6 Solution to Exercises -- 4.7 Bibliographic Notes -- References -- 5. Estimation of Stochastic Models for Finance -- 5.1 Geometric Brownian Motion -- 5.2 Quasi-Maximum Likelihood Estimation -- 5.3 Short-Term Interest Rates Models -- 5.4 Exponential Levy Model -- 5.5 Telegraph and Geometric Telegraph Process -- 5.6 Solution to Exercises -- 5.7 Bibliographic Notes -- References -- 6. European Option Pricing -- 6.1 Contingent Claims -- 6.2 Solution of the Black & Scholes Equation -- 6.3 The Hedging and the Greeks -- 6.4 Pricing Under the Equivalent Martingale Measure -- 6.5 More on Numerical Option Pricing -- 6.6 Implied Volatility and Volatility Smiles -- 6.7 Pricing of Basket Options -- 6.8 Solution to Exercises -- 6.9 Bibliographic Notes -- References -- 7. American Options -- 7.1 Finite Difference Methods -- 7.2 Explicit Finite-Difference Method -- 7.3 Implicit Finite-Difference Method -- 7.4 The Quadratic Approximation -- 7.5 Geske & Johnson and Other Approximations -- 7.6 Monte Carlo Methods -- 7.7 Bibliographic Notes -- References -- 8. Pricing Outside the Standard Black & Scholes Model -- 8.1 The Levy Market Model -- 8.2 Pricing Under the Jump Telegraph Process -- 8.3 Markov Switching Diffusions -- 8.4 The Benchmark approach -- 8.5 Bibliographic Notes -- References -- 9. Miscellanea -- 9.1 Monitoring of the Volatility -- 9.2 Asynchronous Covariation Estimation -- 9.3 LASSO Model Selection -- 9.4 Clustering of Financial Time Series -- 9.5 Bibliographic Notes -- References -- A. How to Guide to R -- A.1 Something to Know Soon About R -- A.2 Objects -- A.3 S4 Objects -- A.4 Functions -- A.5 Vectorization -- A.6 Parallel Computing in R -- A.7 Bibliographic Notes -- References -- B.R in Finance -- B.1 Overview of Existing R Frameworks -- B.2 Summary of Main Time Series Objects in R -- B.3 Dates and Time Handling -- B.4 Binding of Time Series -- B.5 Loading Data From Financial Data Servers -- B.6 Bibliographic Notes -- References -- Index |
| Summary |
"Presents inference and simulation of stochastic process in the field of model calibration for financial times series modeled with continuous time processes and numerical option pricing. Introduces the basis of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them and covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models based on switching models or models with jumps are featured along with new models (Levy and telegraph process modeling) and topics such as; volatilty, covariation, p-variation and regime switching analysis, attention is focused on the calibration of these topics from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Options (Finance) -- Prices
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Probabilities.
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Stochastic processes.
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Time-series analysis.
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Probability
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Stochastic Processes
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probability.
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BUSINESS & ECONOMICS -- Investments & Securities -- General.
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Options (Finance) -- Prices
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Probabilities
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Stochastic processes
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Time-series analysis
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| Form |
Electronic book
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| ISBN |
9781119990079 |
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1119990076 |
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9781119990086 |
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1119990084 |
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9780470745847 |
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0470745843 |
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1283405199 |
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9781283405195 |
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9786613405197 |
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6613405191 |
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