Numerical Methods in Computational Finance. Daniel J. Duffy
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rel="nofollow" href="#ub48681aa-5b26-5df7-a456-e59700bccee0">CHAPTER 23: Multi-Asset Options 23.1 INTRODUCTION AND OBJECTIVES 23.2 BACKGROUND AND GOALS 23.3 THE BIVARIATE NORMAL DISTRIBUTION (BVN) AND ITS APPLICATIONS 23.4 PDE MODELS FOR MULTI-ASSET OPTION PROBLEMS: REQUIREMENTS AND DESIGN 23.5 AN OVERVIEW OF FINITE DIFFERENCE SCHEMES FOR MULTI-ASSET OPTION PROBLEMS 23.6 AMERICAN SPREAD OPTIONS 23.7 APPENDICES 23.8 SUMMARY AND CONCLUSIONS CHAPTER 24: Asian (Average Value) Options 24.1 INTRODUCTION AND OBJECTIVES 24.2 BACKGROUND AND PROBLEM STATEMENT 24.3 PROTOTYPE PDE MODEL 24.4 THE MANY WAYS TO HANDLE THE CONVECTIVE TERM 24.5 ADE FOR ASIAN OPTIONS 24.6 ADI FOR ASIAN OPTIONS 24.7 SUMMARY AND CONCLUSIONS CHAPTER 25: Interest Rate Models 25.1 INTRODUCTION AND OBJECTIVES 25.2 MAIN USE CASES 25.3 THE CIR MODEL 25.4 WELL-POSEDNESS OF THE CIRPDE MODEL 25.5 FINITE DIFFERENCE METHODS FOR THE CIR MODEL 25.6 HESTON MODEL AND THE FELLER CONDITION 25.7 SUMMARY AND CONCLUSION CHAPTER 26: Epilogue Models Follow-Up Chapters 1 to 25 26.1 INTRODUCTION AND OBJECTIVES 26.2 MIXED DERIVATIVES AND MONOTONE SCHEMES 26.3 THE COMPLEX STEP METHOD (CSM) REVISITED 26.4 EXTENDING THE HULL–WHITE: POSSIBLE PROJECTS 26.5 SUMMARY AND CONCLUSIONS
11 Bibliography
12 Index
List of Tables
1 Chapter 7TABLE 7.1 Accuracy of ADE, put option.TABLE 7.2 Accuracy of ADE, call option.TABLE 7.3 Stress-testing ADE, put option.TABLE 7.4 Convection-dominated problems.TABLE 7.5 Testing the CEV Model, (put option).TABLE 7.6 Calculating sensitivities.TABLE 7.7 Early exercise,
2 Chapter 16TABLE 16.1 Output from steps 1–5; data is
List of Illustrations
1 Chapter 2FIGURE 2.1 Continuous and discrete spaces.
2 Chapter 7FIGURE 7.1 Stencil for fully implicit scheme.FIGURE 7.2 Crank–Nicolson and fully explicit stencils.FIGURE 7.3 Trinomial tree model.FIGURE 7.4 Non-uniform mesh.
3 Chapter 11FIGURE 11.1 Region and boundary.FIGURE 11.2 Boundaries for Heston model
4 Chapter 12FIGURE 12.1 Region of integration D.
5 Chapter 13FIGURE 13.1 Mesh generation.
6 Chapter 14FIGURE 14.1 Mesh in (x, t) space.FIGURE 14.2 Special cases.
7 Chapter 15FIGURE 15.1 Padé table for
8 Chapter 16FIGURE 16.1 Motivating divided differences.FIGURE 16.2 Region R and boundary curve C.
9 Chapter 17FIGURE 17.1 Example with three variables.FIGURE 17.2 Example with two variables.
10 Chapter 18FIGURE 18.1 Hopscotch mesh point.
11 Chapter 19FIGURE 19.1 Non-uniform mesh.FIGURE 19.2 Visualisation of ADE process.
12 Chapter 20FIGURE 20.1 Price profile.FIGURE 20.2 Delta profile.FIGURE 20.3 Gamma profile.
13 Chapter 22FIGURE 22.1 Block diagram for software framework.
14 Chapter 23FIGURE 23.1 Error handling and extreme values for the error functions.FIGURE 23.2 Context diagram for Monte Carlo engine.
15 Chapter 25FIGURE 25.1 Direction of information flow (two-dimensional case).FIGURE 25.2 Approximation on the boundary.
Guide
1 Cover
4 Preface