Sample Syllabus


Catalog Description:

This is a course in modeling of the values of assets and financial derivatives and the software implementation of these models for pricing, simulations and scenario analysis. The course includes an introduction to markets and financial derivatives, and a development of the necessary tools from the theories of stochastic processes and parabolic differential equations. An integral part of the course is the use of financial information sources and software packages available on the Internet for modeling and analysis.

Prerequisites: acquaintance with multi-variable calculus and programing in C, C++, and/or Java




Textbook(s)

Required: [WHD ] Willmott, P., Dewynne, J.N. and Howison, S.D. (1999) The Mathe-
matics of Financial Derivatives. A Student Introduction, Cambridge Univ.
Press, ISBN 0-521-49789-2.

Recommended: [H ] Hull, J. (1997) Introduction to Futures and Options Markets, Third Edi-
tion, Prentice Hall. ISBN 0-13-889148-6.
4


Week-By-Week

Week
 Topics Covered
 Reading
 Assignments
1
  • Markets, assets, derivatives.
  • Interest rates and present value.
  • Options, futures, forward contracts, and hedging strategies.
[WHD: Chapter 1] and [H*:Chapters 1, 2, and 6] or [H: Chapters 1,
2, and 7]
2
  •  Probability, Stochastic Processes, Ito calculus
[WHD: Chapters 2 and 4], and [H*: Section 11.3 and Chapter
15] or [H: Section 11.3 (page 253) and Chapter 15]
3
  • Risk and Arbitrage.
  • Option values, pay-offs, and strategies.
  • Put-call parity.
  • The Black-Scholes analysis and the Black-Scholes equation.

 [WHD: Chapter 3] 
4
  • European Options: boundary and ¯nal conditions.
  • Deriving the Black-Scholes formulae.
  • Binary options.
[WHD: Chapter 5]
5
  • Options on dividend-paying assets.
  • Stock indices and currencies.
  • Time dependent parameters.




 [WHD Chapter 6]
6
  • Hedging in practice.
  • Implied volatility
[H Chapters 11, 12, and 13]
7
  • American options
 [WHD: Chapter 7]or [H: Chapter 8].
8
  • Binomial methods 1:
    • The discrete random walk, valuing the option.
    • European options.
[WHD Chapter 10: 1-4]
9
  • Binomial methods 2:
    • American  options
    •  Dividend yields.
[WHD Chapter 10: 5, 6] or [H Chapter 16]
10
  • Finite difference methods  1: Implicit methods: the fully implicit method, Cranck-Nichloson
[WHD Chapter 8: 1-7]
11
  • Finite difference methods. Implicit methods: Error analysis. Stability.
  • Numerics for American options 1.

[WHD Chapter 9]
12
  • Numerics for American options 2
  • Exotics, path-dependent options and barriers
 [WHD Chapter 11, 12, and 13]
13
  • Primer on Options with Transaction Costs
[WHD: Chapter 16]
14
  • Interest Rate Models and Bond Pricing
[WHD: Chapter 17]