Title:
A workout in computational finance
Author:
Aichinger, Michael, 1979-
ISBN:
9781119971917
Personal Author:
Physical Description:
pages cm.
Series:
Wiley finance series
Contents:
Machine generated contents note: 1.Introduction and Reading Guide -- 2.Binomial Trees -- 2.1.Equities and Basic Options -- 2.2.The One Period Model -- 2.3.The Multiperiod Binomial Model -- 2.4.Black-Scholes and Trees -- 2.5.Strengths and Weaknesses of Binomial Trees -- 2.5.1.Ease of Implementation -- 2.5.2.Oscillations -- 2.5.3.Non-recombining Trees -- 2.5.4.Exotic Options and Trees -- 2.5.5.Greeks and Binomial Trees -- 2.5.6.Grid Adaptivity and Trees -- 2.6.Conclusion -- 3.Finite Differences and the Black-Scholes PDE -- 3.1.A Continuous Time Model for Equity Prices -- 3.2.Black-Scholes Model: From the SDE to the PDE -- 3.3.Finite Differences -- 3.4.Time Discretization -- 3.5.Stability Considerations -- 3.6.Finite Differences and the Heat Equation -- 3.6.1.Numerical Results -- 3.7.Appendix: Error Analysis -- 4.Mean Reversion and Trinomial Trees -- 4.1.Some Fixed Income Terms -- 4.1.1.Interest Rates and Compounding -- 4.1.2.Libor Rates and Vanilla Interest Rate Swaps --
Contents note continued: 4.2.Black76 for Caps and Swaptions -- 4.3.One-Factor Short Rate Models -- 4.3.1.Prominent Short Rate Models -- 4.4.The Hull-White Model in More Detail -- 4.5.Trinomial Trees -- 5.Upwinding Techniques for Short Rate Models -- 5.1.Derivation of a PDE for Short Rate Models -- 5.2.Upwind Schemes -- 5.2.1.Model Equation -- 5.3.A Puttable Fixed Rate Bond under the Hull-White One Factor Model -- 5.3.1.Bond Details -- 5.3.2.Model Details -- 5.3.3.Numerical Method -- 5.3.4.An Algorithm in Pseudocode -- 5.3.5.Results -- 6.Boundary, Terminal and Interface Conditions and their Influence -- 6.1.Terminal Conditions for Equity Options -- 6.2.Terminal Conditions for Fixed Income Instruments -- 6.3.Callability and Bermudan Options -- 6.4.Dividends -- 6.5.Snowballs and TARNs -- 6.6.Boundary Conditions -- 6.6.1.Double Barrier Options and Dirichlet Boundary Conditions -- 6.6.2.Artificial Boundary Conditions and the Neumann Case -- 7.Finite Element Methods --
Contents note continued: 7.1.Introduction -- 7.1.1.Weighted Residual Methods -- 7.1.2.Basic Steps -- 7.2.Grid Generation -- 7.3.Elements -- 7.3.1.ID Elements -- 7.3.2.2D Elements -- 7.4.The Assembling Process -- 7.4.1.Element Matrices -- 7.4.2.Time Discretization -- 7.4.3.Global Matrices -- 7.4.4.Boundary Conditions -- 7.4.5.Application of the Finite Element Method to Convection-Diffusion-Reaction Problems -- 7.5.A Zero Coupon Bond Under the Two Factor Hull-White Model -- 7.6.Appendix: Higher Order Elements -- 7.6.1.3D Elements -- 7.6.2.Local and Natural Coordinates -- 8.Solving Systems of Linear Equations -- 8.1.Direct Methods -- 8.1.1.Gaussian Elimination -- 8.1.2.Thomas Algorithm -- 8.1.3.LU Decomposition -- 8.1.4.Cholesky Decomposition -- 8.2.Iterative Solvers -- 8.2.1.Matrix Decomposition -- 8.2.2.Krylov Methods -- 8.2.3.Multigrid Solvers -- 8.2.4.Preconditioning -- 9.Monte Carlo Simulation -- 9.1.The Principles of Monte Carlo Integration --
Contents note continued: 9.2.Pricing Derivatives with Monte Carlo Methods -- 9.2.1.Discretizing the Stochastic Differential Equation -- 9.2.2.Pricing Formalism -- 9.2.3.Valuation of a Steepener under a Two Factor Hull-White Model -- 9.3.An Introduction to the Libor Market Model -- 9.4.Random Number Generation -- 9.4.1.Properties of a Random Number Generator -- 9.4.2.Uniform Variates -- 9.4.3.Random Vectors -- 9.4.4.Recent Developments in Random Number Generation -- 9.4.5.Transforming Variables -- 9.4.6.Random Number Generation for Commonly Used Distributions -- 10.Advanced Monte Carlo Techniques -- 10.1.Variance Reduction Techniques -- 10.1.1.Antithetic Variates -- 10.1.2.Control Variates -- 10.1.3.Conditioning -- 10.1.4.Additional Techniques for Variance Reduction -- 10.2.Quasi Monte Carlo Method -- 10.2.1.Low-Discrepancy Sequences -- 10.2.2.Randomizing QMC -- 10.3.Brownian Bridge Technique -- 10.3.1.A Steepener under a Libor Market Model --
Contents note continued: 11.Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks -- 11.1.Pricing American options using the Longstaff and Schwartz algorithm -- 11.2.A Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments -- 11.2.1.Algorithm: Extended LSMC Method for Bermudan Options -- 11.2.2.Notes on Basis Functions and Regression -- 11.3.Examples -- 11.3.1.A Bermudan Callable Floater under Different Short-rate Models -- 11.3.2.A Bermudan Callable Steepener Swap under a Two Factor Hull-White Model -- 11.3.3.A Bermudan Callable Steepener Cross Currency Swap in a 3D IK/FX Model Framework -- 12.Characteristic Function Methods for Option Pricing -- 12.1.Equity Models -- 12.1.1.Heston Model -- 12.1.2.Jump Diffusion Models -- 12.1.3.Infinite Activity Models -- 12.1.4.Bates Model -- 12.2.Fourier Techniques -- 12.2.1.Fast Fourier Transform Methods -- 12.2.2.Fourier-Cosine Expansion Methods --
Contents note continued: 13.Numerical Methods for the Solution of PIDEs -- 13.1.A PIDE for Jump Models -- 13.2.Numerical Solution of the PIDE -- 13.2.1.Discretization of the Spatial Domain -- 13.2.2.Discretization of the Time Domain -- 13.2.3.A European Option under the Kou Jump Diffusion Model -- 13.3.Appendix: Numerical Integration via Newton-Cotes Formulae -- 14.Copulas and the Pitfalls of Correlation -- 14.1.Correlation -- 14.1.1.Pearson's ρ -- 14.1.2.Spearman's ρ -- 14.1.3.Kendall's τ -- 14.1.4.Other Measures -- 14.2.Copulas -- 14.2.1.Basic Concepts -- 14.2.2.Important Copula Functions -- 14.2.3.Parameter estimation and sampling -- 14.2.4.Default Probabilities for Credit Derivatives -- 15.Parameter Calibration and Inverse Problems -- 15.1.Implied Black-Scholes Volatilities -- 15.2.Calibration Problems for Yield Curves -- 15.3.Reversion Speed and Volatility -- 15.4.Local Volatility -- 15.4.1.Dupire's Inversion Formula --
Contents note continued: 15.4.2.Identifying Local Volatility -- 15.4.3.Results -- 15.5.Identifying Parameters in Volatility Models -- 15.5.1.Model Calibration for the FTSE-100 -- 16.Optimization Techniques -- 16.1.Model Calibration and Optimization -- 16.1.1.Gradient-Based Algorithms for Nonlinear Least Squares Problems -- 16.2.Heuristically Inspired Algorithms -- 16.2.1.Simulated Annealing -- 16.2.2.Differential Evolution -- 16.3.A Hybrid Algorithm for Heston Model Calibration -- 16.4.Portfolio Optimization -- 17.Risk Management -- 17.1.Value at Risk and Expected Shortfall -- 17.1.1.Parametric VaR -- 17.1.2.Historical VaR -- 17.1.3.Monte Carlo VaR -- 17.1.4.Individual and Contribution VaR -- 17.2.Principal Component Analysis -- 17.2.1.Principal Component Analysis for Non-scalar Risk Factors -- 17.2.2.Principal Components for Fast Valuation -- 17.3.Extreme Value Theory -- 18.Quantitative Finance on Parallel Architectures -- 18.1.A Short Introduction to Parallel Computing --
Contents note continued: 18.2.Different Levels of Parallelization -- 18.3.GPU Programming -- 18.3.1.CUDA and OpenCL -- 18.3.2.Memory -- 18.4.Parallelization of Single Instrument Valuations using (Q)MC -- 18.5.Parallelization of Hybrid Calibration Algorithms -- 18.5.1.Implementation Details -- 18.5.2.Results -- 19.Building Large Software Systems for the Financial Industry.
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