MATH 5765/6895, SPRING 2012

Introduction to Mathematical Finance II

Instructor: Jingyi Zhu, LCB 335, 801-581-3236,

Class Schedule: TH: 9:10-10:30 am, JWB 333

Office Hours: Monday 2:00 - 3:30 pm, Thursday 12:30-2:00 pm, or by appointment, LCB 335

Text: S. M. Ross, An Elementary Introduction to Mathematical Finance, Third Edition
(2011), Cambridge University Press, ISBN 978-0-521-19253-8.

Prerequisites: Introduction to Mathematical Finance I (Math 5760)

Topics to be Covered:

  • Exotic options, a brief introduction
  • Monte Carlo simulations and some variance reduction techniques
  • Beyond geometric Brownian motion, some other models
  • Autoregressive models and mean reversion
  • Estimating volatility and covariance, the GARCH model
  • Fundamentals of continuous time finance, Brownian motion revisited
  • Ito's integral, Ito's lemma, and Ito's process
  • Black-Scholes equation derived
  • Martingale and risk-neutral pricing
  • Change of measure and exotic option pricing
  • Introduction to stochastic volatility models
  • Jump diffusion process and models
  • Credit modeling
  • Examples of statistical arbitrage


  • Homework Assignments (70%): taken from the textbook and notes;
  • Take-Home Final (30%): a comprehensive exam that covers all the materials and it will be made available at
    the beginning of the last week of class.

Lecture Notes

Homework Assignments:

Solution Notes: