Matlab is used within nearly all investment banks and is a requirement in most quant job ads. This book enables readers to implement financial and econometric models in Matlab[registered]. All central concepts and theories are illustrated by Matlab[registered] implementations which are accompanied by detailed descriptions of the programming steps needed. Chapter 1 introduces Matlab[registered] and matrix algebra, it serves to make the reader familiar with the use and basic capabilities if Matlab[registered]. The chapter concludes with a walkthrough of a linear regression model, showing how Matlab[registered] can be used to solve an example problem analytically and by the use of optimization and simulation techniques.Chapter 2 introduces expected return and risk as central concepts in finance theory using fixed income instruments as examples, the chapter illustrates how risk measures such as standard deviation, Modified duration, VaR, and expected shortfall can be calculated empirically and in closed form. Chapter 3 introduces the concept of diversification and illustrates how the efficient investment frontier can be derived - a Matlab[registered] is developed that can be used to calculate a given number of portfolios that lie on an efficient frontier, the chapter also introduces the CAPM.Chapter 4 introduces econometric tools: principle component analysis is presented and used as a prelude to yield-curve factor models. The Nelson-Siegel model is used to introduce the Kalman-Filter as a way to add time-series dynamics to the evolution of yield curves over time, time series models, such as Vector Autoregression and regime-switching are also presented. It is supported by a website with online resources where all Matlab[registered] programs referred to in the text can be downloaded. The site also contains lecture slides and answers to end of chapter exercises.
1. Introduction.1.1 Strategic Asset Allocation.1.2 Outline of the Book.2. Essential Elements of Matlab.2.1 Introduction.2.2 Getting started.2.3 Introductorymatrix algebra.2.4 Organising data.2.5 Creating functions.2.5.1 Branching and looping.2.5.2 An example of a simple function.2.5.3 Calling functions in Matlab Ro.2.6 The linear regression.2.6.1 The basic setup.2.6.2 Maximumlikelihood.2.7 Some estimation examples.2.8 A brief introduction to simulations.2.8.1 Generating correlated randomnumbers.3. Fixed-Income Preliminaries.3.1 Introduction.3.2 Spot rates and yields.3.3 Forward rates.3.4 Bond pricing functions.4. Risk and Return Measures.4.1 Introduction.4.2 RiskMeasures.4.2.1 Value-at-risk and Expected Shortfall.4.2.2 Duration and modified duration.4.3 Fixed-Income Returns.5. Term Structure Models.5.1 Introduction.5.2 Not-Necessarily Arbitrage FreeModels.5.2.1 Nelson and Siegel.5.2.2 Svensson and Soderlind.5.3 Arbitrage-FreeModels.5.3.1 Vasicek.5.3.2 Multi-factormodels: an example.6. Asset Allocation.6.1 Introduction.6.2 Efficient portfolios.6.3 Diversification.6.4 Theminimumvariance portfolio.6.5 Asset weight constraints.6.6 The Capital Asset PricingModel.7. Statistical Tools.7.1 Introduction.7.2 The Vector Auto Regression.7.2.1 Order of integration.7.3 Regime switchingmodels.7.3.1 Introduction.7.4 Yield curvemodels in state-space form.7.4.1 The Nelson-Siegelmodel in state-space.7.5 Importance Sampling.7.5.1 Some theory.7.5.2 An example.8. Building graphical user interfaces.8.1 Introduction.8.2 The "guide" development environment.8.3 Creating a simple GUI.8.3.1 Plotting the yield curve.8.3.2 Estimating lambda and yield curve factors.9. Useful Formulas and Expressions.9.1 Introduction.9.2 Matrix operations.9.2.1 Definitions.9.2.2 Sum.9.2.3 Product.9.2.4 Transpose.9.2.5 Symmetricmatrix.9.2.6 The Identitymatrix.9.2.7 Determinant.9.2.8 Rank.9.2.9 Inverse.9.2.10 Trace.9.2.11 Powers.9.2.12 Eigenvalues and eigenvectors.9.2.13 Positive definite.9.2.14 Matrix differentiation.9.3 Decompositions.9.3.1 Triangular.9.3.2 Cholesky.9.3.3 Eigenvalue.9.4 Basic rules.9.4.1 Index rules.9.4.2 Logarithmrules.9.4.3 Simple derivatives.9.4.4 Simple integrals.9.5 Distributions.9.5.1 Normal.9.5.2 Multivariate normal.9.5.3 Vasicek's limiting distribution.9.6 Functions.9.6.1 Linear (affine) function.9.6.2 Quadratic function.9.6.3 General polynominals.9.6.4 Exponential.9.6.5 Logarithm.9.6.6 Error function.9.6.7 Inverse.9.7 Taylor series approximation.9.8 Interest rates, returns and portfolio statistics.9.8.1 Cummulative arithmetic return.9.8.2 Average arithmetic return.9.8.3 Cummulative geometric return.9.8.4 Average geometric return.9.8.5 Compounding of interest rates.9.8.6 Portfolio statistics.
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