Stochastic Simulation and Applications in Finance with Matlab Programs Book

1 Introduction to probability 1

2 Introduction to random variables 9

3 Random sequences 39

4 Introduction to computer simulation of random variables 47

5 Foundations of Monte Carlo simulations 67

6 Fundamentals of quasi Monte Carlo (QMC) simulations 91

7 Introduction to random processes 109

8 Solution of stochastic differential equations 123

9 General approach to the valuation of contingent claims 149

10 Pricing options using Monte Carlo simulations 169

11 Term structure of interest rates and interest rate derivatives 221

12 Credit risk and the valuation of corporate securities 247

13 Valuation of portfolios of financial guarantees 265

14 Risk management and value at risk (VaR) 283

15 Value at risk (VaR) and principal components analysis (PCA) 297

App. A Review of mathematics 315

App. B MATLAB functions 325

References and bibliography 327

Index 333