Contents
Introduction
1 Indices and their derivatives
1.1 What indices are
1.2 Some of the more commonly-used indices
1.3 Current stock indices
1.4 The index derivatives
1.4.1 Index options
2 Stock index derivative pricing model
2.1 The n-dimensional Black-Scholes equation
2.1.1 A stochastic equation for a derivative value
2.1.2 Construction of a riskless portfolio
2.1.3 The terminal conditions
2.2 Analytical solution to the Black-Scholes equation
3 Numerical methods
3.1 Full space-time discretization
3.1.1 Discretization in time
3.1.2 Spatial discretization
3.1.3 The boundary conditions
3.2 The additive operator splitting technique
3.3 The order of the AOS approximation
3.3.1 The forming matrices
3.3.2 Error estimates
3.4 Computational parallelism
Conclusions
References