Financial Modeling

Fall 2009, PSTAT 223A

Tu-Th 2:00-3:15 - HSSB 4201

Jean-Pierre Fouque

		
Office Hours: Wednesday 10:00--12:00 or by appointment

		
		Office: South Hall 5504
		Phone:  893-5637
fouque at pstat.ucsb.edu


TA: Matt Lorig

Discussion Time and Location: Th 5:00 - 5:50; Girv 1106
Office hours: Friday 3:30--4:30, Broida 6122

Agenda:

Midterm exams: October 22 and November 24

Final exam: December 9 (4:00-7:00PM)

Week 1:

  • Thursday September 24: One-period binomial model (2.1). Homework 1 due on Thursday October 8.

    Week 2:

  • September 29: One-period model continued. Risk-neutral probability.
  • October 1: Multi-period binomial model (CRR). Replication and risk-neutral valuation. Read Chapter 2 and Chapter 3.

    Week 3:

  • October 6: Multi-period binomial model (continued). Calibration of the tree.
  • October 8: Calibration of the tree. Convergence and derivation of the Black-Scholes formula. Homework 2 due on Thursday October 22.

    Week 4:

  • October 13: Put/Call parity. Introduction to American options (binomial tree). Brownian motion (definition and characterization).
  • October 15: Stochastic integrals. Ito's formula.

    Week 5:

  • October 20: Ito's processes and stochastic calculus. Homework 3 due October 29: 4.1 to 4.5 p. 59-60.
  • October 22: MIDTERM 1 (on chapter 2 and chapter 4 up to 4.6) in class at 2:00PM, open documents. NO discussion at 5PM.

    Week 6:

  • October 27: Stochastic differential equations. Examples. GBM: estimate mu and sigma.
  • October 29: Derivation of the Black-Scholes PDE and its properties. Homework 4 due November 12: 5.1 and 5.5 to 5.9 p. 75-77.

    Week 7:

  • November 3: Markov property, semigroup, infinitesimal generator, backward Kolmogorov equation, Feynman-Kac formula.
  • November 5: Girsanov Theorem. Risk-neutral valuation.

    Week 8:

  • November 10: Discounted self-financing portfolios under risk-neutral. Representation Theorem.
  • November 12: Generalizations: dividends, time-varying volatility. Implied volatility surface. Homework 5 due November 19: 9.1, 9.2, 9.3 p. 130-131.

    Week 9:

  • November 17: Local volatility models. Dupire's PDE and formula.
  • November 19: Greeks. Knock-out options (by Matt Lorig).

    Week 10:

  • November 24: MIDTERM 2
  • November 26: THANKSGIVING

    Week 11:

  • December 1:
  • December 3:

    Course Outline

  • Introduction to financial derivatives - One-period model (2 lectures).
  • Cox-Ross-Rubinstein discrete binomial model (2).
  • Stochastic calculus (4).
  • Black-Scholes continuous time model (2).
  • PDE approach (2).
  • Risk-neutral valuation (2).
  • Exotic options (4).

    Prerequisites: PSTAT 213 A-B-C Introduction to Probability Theory and Stochastic Processes

    Grading: Homework 30%, Midterms(2) 40%, Final 30%

    TEXT:
    Tomas Bjork, Arbitrage Theory in Continuous Time. Oxford, Second Edition (2004).