Pricing Financial Instruments The Finite Difference Method,9780471197607

Pricing Financial Instruments The Finite Difference Method

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Edition: 1st
ISBN13: 9780471197607
ISBN10: 0471197602
Format: Hardcover
Pub. Date: 2000-04-21
Publisher(s): Wiley
List Price: $130.00

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Summary

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Author Biography

<b>DOMINGO TAVELLA, Ph.D.</b>, is President of Octanti Associates, a consulting firm in risk management and financial systems design. He is the founder and chief editor of the Journal of Computational Finance, and has pioneered the application of advanced numerical techniques in pricing and risk analysis in the financial and insurance industries. Before founding Octanti Associates, Dr. Tavella was director of financial engineering at Integral Development Corporation and vice president at Bankers Trust Securities. Prior to that, he was a scientist at Stanford University and NASA Ames Research Center.

Table of Contents

Introduction
1(22)
Stochastic Processes
3(10)
Markov Processes
5(3)
Stochastic Differential Equations
8(1)
Ito's Formula
9(1)
Ito's Formula for Processes with Jumps
10(3)
Arbitrage Pricing Theory
13(8)
Change of Measure
16(5)
References
21(2)
The Pricing Equations
23(38)
European Derivatives
24(6)
Hedging Portfolio Approach
24(3)
Feynman-Kac Approach
27(3)
The Pricing Equation in the Presence of Jumps
30(9)
An Application of Jump Processes: Credit Derivatives
34(3)
Defaultable Bonds
37(1)
Full Protection Credit Put
38(1)
American Derivatives
39(6)
Relationship between European and American Derivatives
40(2)
American Options as Dynamic Optimization Problems
42(1)
Conditions at Exercise Boundaries
43(1)
Linear Complementarity Formulation of American Option Pricing
44(1)
Path Dependency
45(3)
Discrete Sampling of Path Dependency
47(1)
Dimensionality Reduction
48(8)
Reformulating the Underlying Processes in a Different Measure
49(1)
Currency Translated Options
50(6)
Equations for the Hedging Parameters
56(4)
Computation of Greeks by Direct Discretization
57(1)
Computation of Greeks through Their Governing Equations
57(3)
References
60(1)
Analysis of Finite Difference Methods
61(49)
Motivation
61(6)
Constructing Finite Difference Approximations
67(3)
Stability Analysis: Matrix Approach
70(20)
Space Discretization
71(2)
Time Discretization
73(4)
Analysis of Specific Algorithms
77(9)
Eigenvalue Analysis of the Black-Scholes Equation
86(4)
Stability Analysis: Fourier Approach
90(3)
Implementation of the Time Advancement
93(7)
Solving Sparse Systems of Linear Equations
94(6)
Finite Difference Approach to American Options
100(5)
The Linear Complementarity Problem
101(4)
Distortions Induced by Discretization
105(2)
Strategies for Complex Derivative Structures
107(1)
References
108(2)
Special Issues
110(46)
Effect of Payoff Discontinuities on Convergence
110(4)
Implementing Jump Conditions
114(6)
Boundary Conditions
120(12)
Boundary Conditions in One Dimension
121(9)
Boundary Conditions in Multiple Dimensions
130(2)
Continuous and Discrete Sampling Models for Path-Dependent Options
132(9)
Continuous Sampling
132(4)
Discrete Sampling
136(5)
Performance of Solvers for Multidimensional Problems
141(6)
Numerical Solution of PIDEs: Jump-Diffusion and Pure Jump Models
147(8)
References
155(1)
Coordinate Transformations
156(27)
One-Dimensional, Time-Independent Transformations
157(15)
Transformations Place Grid Points at Selected Positions
160(7)
Transformations That Concentrate Grid Points
167(5)
One-Dimensional, Time-Dependent Transformations
172(1)
Multidimensional, Time-Independent Transformations
173(9)
Factored Multidimensional, Time-Independent Transformations
174(1)
General Multidimensional, Time-Independent Transformations
175(2)
Multidimensional Linear Transformations
177(5)
References
182(1)
Numerical Examples
183(48)
Barrier Options
183(13)
Time-Dependent Barriers
183(4)
Nonuniform Grids and Discrete Sampling
187(9)
Discretely Sampled Parisian Options
196(6)
A Leveraged Knockin Put
202(4)
Discretely Sampled Asian Options
206(6)
Stochastic Volatility
212(2)
Convertible Bond
214(4)
Simple Fixed Income Instruments: Forward Swap
218(5)
Credit Derivatives
223(5)
References
228(3)
Index 231

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