Financial Modeling

Winter 2018, PSTAT 223B

M-W 9:30-10:45, HSSB 1207

Jean-Pierre Fouque

fouque at pstat.ucsb.edu

Office Hours: W 11am-12pm South Hall 5504 or by appointment

Agenda:

Midterm 1: Wednesday February 14

Midterm 2: Wednesday March 14

Week 1 (classes cancelled due to final exams of Fall quarter):

  • January 8: No class.
  • January 10: No class

    Week 2:

  • January 15: Holiday.
  • January 17: One period models. Arbitrage. Replication. Risk-neutral valuation.

    Week 3:

  • January 22: Multi-period models.
  • January 24: Black-Scholes model. Self-financing portfolios and no-arbitrage pricing (Chapters 6 and 7). HW1 due Monday February 5: p. 63-64: 4.2 and 4.5, p. 80-82: 5.5, 5.8, 5.10, 5.11, p. 91: 6.1

    Week 4:

  • January 29: Black-Scholes formula. Breeden-Litzenberger formula. Carr-Madan formula. Implied volatility. HW2 due Monday February 12: p. 113: 7.2, 7.4, 7.5 and p. 134-136: 9.1, 9.2, 9.3, 9.10
  • January 31: Breeden-Litzenberger formula. Carr-Madan formula. Local volatility models and Dupire formula.

    Week 5:

  • February 5: Local volatility models and Dupire formula. HW3 due Wednesday February 21: p. 281: 18.1-4
  • February 7: Stochastic volatility models.

    Week 6:

  • February 12: Stochastic volatility models continued.
  • February 14: Midterm 1 open books/notes.

    Week 7:

  • February 19: Holiday.
  • February 21: Dividends. Bonds and Interest Rates. HW4 due Monday February 26: p. 246: 16.6 and 16.8. Read Section 16.1

    Week 8:

  • February 26: Bonds and Interest Rates (continued). HW5 due Monday March 5: p. 386: 24.1-5 and p. 287: 24.7
  • February 28: Forward rates, HJM model.

    Week 9:

  • March 5: Bond options. Forward measure.
  • March 7: Poisson processes, intensities , by Michael Zhang.

    Week 10:

  • March 12: Credit risk, default modeling (structural and intensity-based).
  • March 14: Midterm 2 open books/notes.

    Course Outline

    An introduction to stochastic models in finance with applications to valuation and hedging of derivatives in equity, fixed income, and credit markets, and to portfolio allocation.

    Prerequisites:

  • PSTAT 213 A-B-C Introduction to Probability Theory and Stochastic Processes (or equivalent)

  • PSTAT 223A Stochastic Calculus and Applications (or equivalent)

    TEXT:
    Arbitrage Theory in Continuous Time by Tomas Bjork, 3rd ed, Oxford 2009