This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory.

It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. 

Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. 

Moreover, there are three appendices with material that is supposed to be known. 

Appendix I contains a comprehensive review of linear algebra, including all the proofs. 

Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. 

Therefore, this book is uniquely self-contained.

1. Introduction

2. Option valuation preliminaries

3. Random variables 

4. Computer simulation 

5. Asset price movement 

6. Asset price model: part I 

7. Asset price model: part II 

8. Black Scholes PDE and formulas 

9. More on hedging 

10. The Greeks 

11. More on the Black Scholes formulas 

12. Risk neutrality 

13. Solving a nonlinear equation 

14. Implied volatility 

15. The Monte Carlo method 

16. The binomial method 

17. Cash-or-nothing options 

18. American options 

19. Exotic options 

20. Historical volatility 

21. Monte Carlo part II: variance reduction by antithetic variates 

22. Monte Carlo part III: variance reduction by control variates 

23. Finite difference methods 

24. Finite difference methods for the Black Scholes PDE.

Desmond J. Higham (Higham, Desmond J.)

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