Derivative Securities and Difference Methods [Hardback]by You-Ian Zhu and Xiaonan Wu and I-Liang Chern and Taiwan Taipei
Usually ships within 6 to 8 working days Description of Derivative Securities and Difference MethodsThis book studies pricing financial derivatives with a partial differential equation approach. The treatment is mathematically rigorous and covers a variety of topics in finance including forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, lookback options, interest rate models, interest rate derivatives, swaps, caps, floors, and collars. Each chapter concludes with exercises.Title Information
Write a review of this book Customer Reviews from AmazonContents of Derivative Securities and Difference MethodsPART I: Partial Differential Equations in Finance1. Introduction 1.1 Assets 1.2 Derivative Securities Problems 2. Basic Options 2.1 Asset Price Model and Ito's Lemma 2.2 Derivation of the Black–Scholes Equation 2.3 Two Transformations on the Black–Scholes Equation 2.4 Solutions of European Options 2.5 American Option Problems as LC Problems 2.6 American Option Problems as FBPs 2.7 Equations for Some Greeks 2.8 Perpetual Options 2.9 General Equations for Derivatives 2.10 Jump Conditions 2.11 More Arbitrage Theory Problems 3. Exotic Options 3.1 Introduction 3.2 Barrier Options 3.3 Asian Options 3.4 Lookback Options 3.5 Multi-Asset Options 3.6 Some Other Exotic Options Problems 4. Interest Rate Derivative Securities 4.1 Introduction 4.2 Bonds 4.3 Some Explicit Solutions of Bond Equations 4.4 Inverse Problem on the Market Price of Risk 4.5 Application of Bond Equations 4.6 Multi-Factor Interest Rate Models 4.7 Two-Factor Convertible Bonds Problems PART II: Numerical Methods for Derivative Securities 5. Basic Numerical Methods 5.1 Approximations 5.2 Solution of Systems and Eigenvalue Problems 5.3 Finite-Difference Methods 5.4 Stability and Convergence Analysis 5.5 Extrapolation of Numerical Solutions 5.6 Determination of Parameters in Models Problems Projects 6. Initial-Boundary Value and LC Problems 6.1 Explicit Methods 6.2 Implicit Methods 6.3 Singularity-Separating Method 6.4 Pseudo-Spectral Methods Problems Projects 7. Free-Boundary Problems 7.1 SSM for Free-Boundary Problems 7.2 Implicit Finite-Difference Methods 7.3 Pseudo-Spectral Methods Problems Projects 8. Interest Rate Modelling 8.1 Inverse Problems 8.2 Numerical Results of One-Factor Models 8.3 Pricing Derivatives with Multi-Factor Models Problems Projects References Index |
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