CSI 779 / STAT 789

Topics in Computational Statistics:

Statistical Modeling of Financial Data

Fall, 2006

Mondays 4:30 to 7:10.

207 Innovation Hall

Text: Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance, by Domingo Tavella (2002).
The general flow of the course follows this text, but we will skip around alot, especially in the coverage of Chapter 2, which we will spread over several weeks, while introducing other topics.

This is not a distance-learning class. I spend a lot of time developing notes that I will post on the web, but it is not to be assumed that these posted notes cover everything covered in the class.

Schedule

• August 28
  Introductory discussion.
  Stock prices; puts and calls.
  Math preliminaries (Chapter 2).
  Brief intro to R.
  Methods in simulation (Chapter 4).
  Lecture notes.
• September 4
  Labor Day holiday; no class
  Assignment 1 to turn in.
• September 11
  Sources of financial data; data analysis q-q plots.
  Monte Carlo methods.
  Stochastic processes.
  Assignment: read Chapter 2.
  Lecture notes.
• September 18
  Wiener processes.
  Stochastic integrals.
  Pricing in continuous time.
  Assignment: read Chapter 3.
  Assignment 2 to turn in.
  Lecture notes.
• September 25
  Estimation of parameters in pricing models.
  Stochastic differential equations.
  Stochastic calculus.
  Assignment 3 to turn in.
  Lecture notes.
• October 2
  Changes of measure.
  Lecture notes.
  More basics of derivatives.
  Lecture notes.
• October 10 Tuesday
  Expectations in stochastic processes.
  Jump processes.
  Lecture notes.
  Volatility and trading activity in futures contracts.
  Stochastic differential equations for pricing.
  Assignment 4 to turn in.
• October 16
  Brief discussions of projects.
  Assumptions in pricing financial assets.
  Lecture notes.
• October 23
  Replicating portfolios. Self-financing.
  Review; wrap up some loose ends.
• October 30
  Midterm exam
  
• November 6
  Review exam.
  Black-Scholes formula.
  The volatility surface.
  Assignment: read Chapter 3 (again!).
  Assignment 5 to turn in.
  Lecture notes.
• November 13
  Brief discussions of projects.
  More on the Black-Scholes model.
  Assignment: read Chapter 5.
  Lecture notes.
• November 20
  The greeks.
  Monte Carlo methods; European-style and American-style options.
  Assignment: read Chapter 6.
  Assignment 6 to turn in.
  Lecture notes.
• November 27
  More on Monte Carlo and other numerical methods.
  Assignment: read Chapter 7.
  The CBOE Volatility Index.
  Lecture notes.
• December 4
  Final presentations of projects.
  Review; wrap up some loose ends.
  Lecture notes.
  Handout takehome exam.
• December 11
  University reading day; make-up day for project presentations.
  

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• December 18
  Takehome exam due.
  Inclass final exam. 4:30pm-7:15pm