Quantitative Methods in Derivatives Pricing : An Introduction to Computational Finance
Domingo. Tavella
Bok Engelsk 2003 · Electronic books.
| Annen tittel | |
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| Utgitt | New York : : Wiley, , 2003.
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| Omfang | 1 online resource (305 p.)
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| Opplysninger | Description based upon print version of record.. - Quantitative Methods in derivatives pricing; preface; acknowledgments; contents; CHAPTER 1 Arbitrage and Pricing; The Pricing Problem; Arbitrage; State Prices; Present Value as an Expectation of Future Values; CHAPTER 2 Fundamentals of Stochastic Calculus; Basic Definitions; Probability Space; Sample Space; Filtration and the Revelation of Information; Probability Measure; Random Variables; Stochastic Process; Measurable Stochastic Process; Adapted Process; Conditional Expectation; Martingales; Wiener Process; First Variation of a Differentiable Function; First Variation of the Wiener Process. - Brownian Bridge ConstructionGenerating Scenarios with Brownian Bridges; Joint Normals by the Choleski Decomposition Approach; Quasi-Random Sequences; The Concept of Discrepancy; Discrepancy and Convergence: The Koksma-Hlawka Inequality; Proper Use of Quasi-Random Sequences; Interest Rate Scenarios; HJM for Instantaneous Forwards; LIBOR Rate Scenarios; Principal Component Analysis to Approximate Correlation Matrices; CHAPTER 5 European Pricing with Simulation; Roles of Simulation in Finance; Monte Carlo in Pricing; Monte Carlo in Risk Management; The Workflow of Pricing with Monte Carlo. - Estimators. - Full Protection Credit PutAmerican Derivatives; Relationship between European and American Derivatives; American Options as Dynamic Optimization Problems; Conditions at Exercise Boundaries; Linear Complementarity Formulation of American Option Pricing; Path Dependency; Discrete Sampling of Path Dependency; CHAPTER 4 Scenario Generation; Scenario Nomenclature; Scenario Construction; Exact Solution Advancement; Sampling from the Joint Distribution of the Random Process; Generating Scenarios by Numerical Integration of the Stochastic Differential Equations; Brownian Bridge. - Martingale Representation TheoremProcesses with Jumps; The Poisson Jump Model; Defining a Pure Jump Process; Defining a Jump-Diffusion Process; Ito's Lemma in the Presence of Jumps; CHAPTER 3 Pricing in Continuous Time; One-Dimensional Risk Neutral Pricing; Multidimensional Market Model; Extension to Other Normalizing Assets; Deriving Risk-Neutralized Processes; The Pricing Equation; European Derivatives; Hedging Portfolio Approach; Feynman-Kac Approach; The Pricing Equation in the Presence of Jumps; An Application of Jump Processes: Credit Derivatives; Defaultable Bonds. - Second Variation of a Differentiable FunctionSecond Variation of the Wiener Process; Products of Infinitesimal Increments of Wiener Processes; Stochastic Integrals; Mean Square Limit; Ito Integral; Properties of the Ito Integral; Ito Processes; Multidimensional Processes; Multidimensional Wiener Processes; Multidimensional Ito Processes; Ito's Lemma; Multidimensional Ito's Lemma; Stochastic Differential Equations; Moments of SDE Solutions; SDE Commonly Used in Finance; The Markov Property of Solutions of SDE; The Feynman-Kac Theorem; Measure Changes; Girsanov Theorem. - This book presents a cogent description of the main methodologies used in derivatives pricing. Starting with a summary of the elements of Stochastic Calculus, Quantitative Methods in Derivatives Pricing develops the fundamental tools of financial engineering, such as scenario generation, simulation for European instruments, simulation for American instruments, and finite differences in an intuitive and practical manner, with an abundance of practical examples and case studies. Intended primarily as an introductory graduate textbook in computational finance, this book will also serve as a refer
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0471394475
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