Numerical partial differential equations in finance explained : an introduction to computational finance

1 Financial Option Valuation -- 1.1 Financial Options -- 1.2 The Black-Scholes PDE -- 2 Partial Differential Equations -- 2.1 Convection-Diffusion-Reaction Equations -- 2.2 The Model Equation -- 2.3 Boundary Conditions -- 2.4 Notes and References -- 3 Spatial Discretization I -- 3.1 Method of Lines -- 3.2 Finite Difference Formulas -- 3.3 Stability -- 3.4 Notes and References -- 4 Spatial Discretization II -- 4.1 Boundary Conditions -- 4.2 Nonuniform Grids -- 4.3 Nonsmooth Initial Data -- 4.4 Mixed Central/Upwind Discretization -- 4.5 Notes and References -- 5 Numerical Study: Space -- 5.1 Cell Averaging -- 5.2 Nonuniform Grids -- 5.3 Boundary Conditions -- 6 The Greeks -- 6.1 The Greeks -- 6.2 Numerical Study -- 6.3 Notes and References -- 7 Temporal Discretization -- 7.1 The -Methods -- 7.2 Stability and Convergence -- 7.3 Maximum Norm and Positivity -- 7.4 Notes and References -- 8 Numerical Study: Time -- 8.1 Explicit Method -- 8.2 Implicit Methods -- 8.3 Notes and References -- 9 Cash-or-Nothing Options -- 10 Barrier Options -- 11 American-Style Options -- 11.1 American-Style Options -- 11.2 LCP Solution Methods -- 11.3 Numerical Study -- 11.4 Notes and References -- 12 Merton Model -- 12.1 Merton Model -- 12.2 Spatial Discretization -- 12.3 IMEX Schemes -- 12.4 Numerical Study -- 12.5 Notes and References -- 13 Two-Asset Options -- 13.1 Two-Asset Options -- 13.2 Spatial Discretization -- 13.3 ADI Schemes -- 13.4 Numerical Study -- 13.5 Notes and References -- Appendix A: Wiener Process -- Appendix B: Feynman-Kac Theorem -- Appendix C: Down-and-Out Put Option Value -- Appendix D: Max-of-Two-Assets Call Option Value -- Bibliography -- Index.