Summer 2012 STATS 237 Theory of Investment Portfolios and Derivative Securities

Tuesday Thursday 11am-12:15pm.

Room HUANG 18.

Instructor:

Isabelle Camilier

Room 383 FF (math building)

Email: camilier (at) stanford (dot) edu

Please put 'Stats 237' in the object of your email.

Office hours:

Mondays 3:15 pm-4:45 pm and Wednesdays 11am-12, or by appointment (email me).

Course Assistant:

Victor Hu

Email: vhu (at) stanford (dot) edu

Office hours: Wednesdays 2-5 pm.

Room: Sequoia 238.

Course Description

In this course, we first focus on investment portfolios, asset returns, their volatilities, and measures of market risk. We introduce to Markowitz's portfolio theory and various pricing models - including capital asset pricing model.

Then we cover option pricing. Geometric random walk and Brownian motion as models of risky assets. Self-financing replicating portfolios. Black-Scholes pricing of European options. Implied volatility and the Greeks. We also address valuation of American options in discrete time.

Prerequisites: At least one probability class. You should be familiar with random variables: discrete random variables (such as binomial random variables), continuous random variables (especially Gaussian random variables) and computing expectations.

Textbooks (optional)

• Statistical models and methods for financial markets by Lai and Xing (chapters 3 and 8)
• Arbitrage Theory in Continuous time by Bjork.
• Options, Futures and other derivatives by Hull

Assignments

Grades will be based on the following:

Homework (60 %) There will be four assignments, each consisting of several problems.

Final exam (40%) take-home.

Software

You may use Matlab or R (www.cran.r-project.org)

Syllabus

Week 1 Introduction.

Weeks 2 Investment models (Markowitz's portfolio theory, CAPM)

Week 3 Discrete time models.

Weeks 4-8 Continuous time finance. Option pricing.

Schedule

June 26: Introduction. Definitions. Assets, asset returns. Lai and Xing chapter 3. Derivatives, call and put options. Hull 1, 9.1-9.4 .

June 28: Investment portfolios. Markowitz's portfolio theory

July 3: Capital Asset Pricing Model (CAPM). Estimation, empirical studies. (Lai&Xing 3.3).

July 5: Multifactor pricing models. (Lai&Xing 3.4).

July 10: Arbitrage. Hull 4.2, 10,11. Call-put parity and data. (Lai&Xing 8.1).

July 12: Discrete time models (binomial trees). Martingales. Hull 12, 20.1, 20.2. HW1 due .

July 17: Optiom pricing in binomial trees. Pricing American options.

July 19: Convergence towards continuous time models. Continuous time models.

July 24:Gaussian random variables. Brownian motion, stochastic processes. Ito formula.

July 26: Black-Scholes PDE. Black-Scholes formula. HW2 due.

July 31: Black-Scholes pricing, continued.

August 2: Greeks. HW3 due.

August 7:Implied volatility and time-series. (Lai&Xing 8.2).

August 9: Stochastic volatility. (Lai&Xing 8.3). HW 4 due.

August 14: Review.

August 16: Review. Final due.