Option Pricing and Estimation of Financial Models with R.
Stefano M. Iacus
Bok Engelsk 2011 · Electronic books.
| Utgitt | Chichester. : Wiley , cop. 2011
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| Omfang | 1 online resource (474 pages)
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| Utgave | 1st ed.
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| Opplysninger | Intro -- Option Pricing and Estimation of Financial Models with R -- Contents -- Preface -- 1 A synthetic view -- 1.1 The world of derivatives -- 1.1.1 Different kinds of contracts -- 1.1.2 Vanilla options -- 1.1.3 Why options? -- 1.1.4 A 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 The 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 The 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 Itô formula -- 3.14 More properties and inequalities for the Itô 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 Lévy processes -- 3.18.1 Lévy-Khintchine formula -- 3.18.2 Lévy jumps and random measures -- 3.18.3 Itô-Lévy decomposition of a Lévy process -- 3.18.4 More on the Lévy measure -- 3.18.5 The Itô formula for Lévy processes -- 3.18.6 Lévy processes and martingales -- 3.18.7 Stochastic differential equations with jumps -- 3.18.8 Itô formula for Lévy 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 An 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 Lévy 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 The special case of the CIR model -- 5.3.2 Ahn-Gao model -- 5.3.3 Aït-Sahalia model -- 5.4 Exponential Lévy model -- 5.4.1 Examples of Lévy 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 The main ingredients of option pricing -- 6.1.2 One period market -- 6.1.3 The 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 The Monte Carlo approach -- 6.2.5 Sensitivity of price to parameters -- 6.3 The δ-hedging and the Greeks -- 6.3.1 The hedge ratio as a function of time -- 6.3.2 Hedging of generic options -- 6.3.3 The density method -- 6.3.4 The numerical approximation -- 6.3.5 The 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 An 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 The 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 The Lévy market model -- 8.1.1 Why the Lévy market is incomplete? -- 8.1.2 The Esscher transform -- 8.1.3 The mean-correcting martingale measure -- 8.1.4 Pricing of European options -- 8.1.5 Option pricing using Fast Fourier Transform method -- 8.1.6 The 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 The 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 The least squares approach -- 9.1.2 Analysis of multiple change points -- 9.1.3 An 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 A modified quasi-MLE -- 9.1.7 First- and second-stage estimators -- 9.1.8 Numerical example -- 9.2 Asynchronous covariation estimation -- 9.2.1 Numerical example -- 9.3 LASSO model selection -- 9.3.1 Modified LASSO objective function -- 9.3.2 Adaptiveness of the method -- 9.3.3 LASSO identification of the model for term structure of interest rates -- 9.4 Clustering of financial time series -- 9.4.1 The Markov operator distance -- 9.4.2 Application to real data -- 9.4.3 Sensitivity to misspecification -- 9.5 Bibliographical notes -- References -- APPENDICES -- A 'How to' guide to R -- A.1 Something to know first about R -- A.1.1 The workspace -- A.1.2 Graphics -- A.1.3 Getting help -- A.1.4 Installing packages -- A.2 Objects -- A.2.1 Assignments -- A.2.2 Basic object types -- A.2.3 Accessing objects and subsetting -- A.2.4 Coercion between data types -- A.3 S4 objects -- A.4 Functions -- A.5 Vectorization -- A.6 Parallel computing in R -- A.6.1 The foreach approach -- A.6.2 A note of warning on the multicore package -- A.7 Bibliographical notes -- References -- B R in finance -- B.1 Overview of existing R frameworks -- B.1.1 Rmetrics -- B.1.2 RQuantLib -- B.1.3 The quantmod package -- B.2 Summary of main time series objects in R -- B.2.1 The ts class -- B.2.2 The zoo class -- B.2.3 The xts class -- B.2.4 The irts class -- B.2.5 The timeSeries class -- B.3 Dates and time handling -- B.3.1 Dates manipulation -- B.3.2 Using date objects to index time series -- B.4 Binding of time series -- B.4.1 Subsetting of time series -- B.5 Loading data from financial data servers -- B.6 Bibliographical notes -- References -- Index.. - Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series 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.
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| Emner | Options (Finance) -- Prices.
Probabilities. Stochastic processes. Time-series analysis. opsjoner spekulasjon finansøkonomi økonomiske modeller statistikk |
| Sjanger | |
| Dewey | 332.6453015 . - 332.6453
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| ISBN | 0470745843. - 9780470745847
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