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].
  11. Example VB Code for linking to C++ [Spreadsheet and DLL].
  12. C++ code for creating DLL [Zip file].
  13. Explicit Finite-Difference Method [Spreadsheet]
  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]
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    2. Take-home exam question with solution.