## MSc in Mathematics and Finance

### Course material by M.H.A. Davis

#### Numerical Methods in Finance, 2008-09

1. Summary Course Notes, Section I.
2. Complete lecture slides. (Note: these incude a lot of material not covered in the lectures.)
3. Lecture slides on Monte Carlo (Zheng).
4. Problems 1 with selected solutions.
5. Problems 2 (assessed) with note on the cubic spline formulas.
6. Problems 3 with selected solutions.
7. Problems 4.
8. Problems 5 (assessed).
9. Problems 6, with selected solutions.
10. VB Code for Binomial Tree [Spreadsheet].
12. C++ code for creating DLL [Zip file].
14. Black-Scholes Barrier Option Formula.
15. Inverting the distribution function.
16. Monte Carlo Greeks.
17. Revision Checklist.
18. Sample exam question.
19. January 2009 Examination paper, solutions

#### Stochastic Differential Equations and Interest Rate Models, 2008

1. Course Outline.
2. Problems 1 .
3. Problems 2.
4. Linear Stochastic Differential Equations [PDF].
5. Problems 3, Solutions.
6. Trinomial tree implementation of Hull-White [PDF]
7. Hull-White Swaption formula [PDF]
8. Group project Groups, Specification, Zip file.
9. Problems 4.
10. Revision checklist.
11. Examination 2006 paper, solutions.
12. Examination 2007 paper, solutions.

#### Lectures on Real Analysis

1. Lecture notes [PDF]
2. Problems [PDF]
3. Solutions to selected problems [PDF]

#### Stochastic Processes I, 2004-2005

1. Problems 0 [PDF] , Code [PDF], Solutions [PDF]
2. Problems 1 [PDF]
3. Problems 2 [PDF]
4. Problems 3 [PDF]
5. Take-home Questions 1 [PDF]
6. Construction of Lebesgue measure [PDF]
7. Inverting the distribution function [PDF]
8. Construction of Brownian Motion [PDF]
9. Revision checklist [PDF]
10. Examination paper, January 2002 [PDF] and solutions [PDF]
11. Examination paper, January 2003, with solutions [PDF]
12. Examination paper, January 2004, with solutions [PDF]
13. Examination paper, January 2005, with solutions [PDF]

#### Mathematical Option Pricing

1. Course outline [PDF]
2. Mathematical Option Pricing (complete notes, January 2006) [PDF]
3. Problems 1 [PDF] and solutions [PDF]
4. Problems 2 [PDF] and solutions [PDF]
5. Problems 3 [PDF]
6. Problems 4 [PDF] and solutions [PDF]
7. Revision Checklist [PDF]
8. Robustness of Black-Scholes Hedging [PDF]
9. Black-Scholes Hedging Spreadsheet [Excel Workbook]
10. Spreadsheet on Importance Sampling [Excel Workbook]
11. Take-home exam question April 2002 [PDF]
12. Take-home exam project code [Zip]
13. Take-home exam project report by Albert Chan [DOC]
14. 2001 Examination Paper [PDF] and solutions [PDF]
15. 2002 Examination Paper [PDF] and solutions [PDF]
16. 2003 Examination Paper [PDF] and solutions [PDF]
17. 2004 Examination Paper [PDF] and solutions [PDF]

#### Projects

1. Project topics 2001 [Web Page]