FIN 285a: Computer Simulations and Risk Assessment

Instructor

TA

Times:

Course Description

Recent advances in both computing power and financial theory are bringing us ever closer to quantifying, and even to some extent, controlling risk. This course provides a unifying framework for analyzing risk from a computer simulation perspective. A common set of computer tools will be applied across several different financial applications ranging from options pricing to portfolio design. Extensive time will be spent on Value at Risk which is a standard for measuring risk in large financial institutions. Computationally intensive methods such as bootstrapping, and monte-carlo analysis will be used extensively throughout the course. The course will also cover several modern approaches to risk which include tail indices, copulas, and financial system networks, all of which can be used in assessing the probability of market distress. Finally, a few examples of agent-based simulations will be used to demonstrate basic ideas of how correlated behavior can occur endogenously in large financial systems.

Learning Goals

  1. Ability to apply computational statistical methods such as bootstrapping, and monte-carlo to questions of risk measurement in financial settings.
  2. Understand how to implement small programs in the matlab programming language for use in financial analysis.
  3. Assess the confidence of various risk measures given available data sets.
  4. Learn how to quantify the impact of ``tail risk'' in many sitautions.
  5. This course can be a rough preparation (with some more reading) for taking the financial risk manager (FRM) exam from the Global Association of Risk Professionals (GARP).

Prerequisites

FIN 201, or a basic knowledge of finance is essential. Fin 270 (Options and derivatives) would also be useful, but it is not required. Finally, a basic working knowledge of statistics is important too. You need to know concepts such as means, variances and distributions. A standard undergraduate course in mathematical statistics would cover this, or the IBS module 210f. Although computer skills will be taught in the course, some enthusiasm for programming will be useful. The course also assumes basic calculus equivalent to about 1 semester of calculus at the undergraduate level.

This course is designed for 2nd year IBS masters students (MA, MSF, MBAi). PhD students may also find some of the content useful as well.

Required Readings:

  1. Danielsson, Financial Risk Forecasting, Wiley, 2011.
  2. Marthinsen, Risk Takers, Second Edition, Addison-Wesley.
  3. Griffiths, Matlab Lecture Notes.

Recommended Readings

  1. Good, Resampling Methods, Third Edition, Birkhauser, 2006.
  2. Jorion, Value at Risk, Third Edition, Wiley.
  3. Jorion, Financial Risk Manager Handbook, fifth edition, Wiley, 2009.
  4. Hanselman and Littlefield, Mastering Matlab 7, Prentice Hall.
  5. Bernstein, Against the Gods, Wiley.

Required Software

Matlab programming language (student edition). Use the mathworks web site, www.mathworks.com. Also, you will need the statistics toolbox. This is also available on the IBS computer cluster.

Grading

Grades will be based on problem sets (20%), a midterm exam (30%), a group project (20%), and a final exam (30%). The group project is due on the last day of class, Monday, December 12th. The Midterm will be Wednesday, October 26th. (Start of module II.) The final exam will take place, Wednesday, Dec 14th, 6:00-9:00pm, (X3 block).

Communications

You are responsible for all announcements and materials in class. Also, much of the information in class will be sent over Latte and the class website.

Rules specific to Fin285

  1. Exams
    1. Your own work.
    2. Closed book (no notes).
    3. No laptops, no cell phones, no pda's.
  2. Problem sets
    1. Hand in your own work.
    2. Can talk and assist each other.
    3. Use all resources.
  3. Group projects
    1. Own work for the group.
    2. Hand in one writeup per group.
  4. Laptops: Please bring to class if you want to.

Academic Honesty

You are expected to be familiar with and to follow the University's policies on academic integrity (see http://www.brandeis.edu/studentlife/sdc/ai/). Instances of alleged dishonesty will be forwarded to the Office of Campus Life for possible referral to the Student Judicial System. Potential sanctions include failure in the course and suspension from the University.

Disability Statement

If you are a student with a documented disability on record at Brandeis University and wish to have a reasonable accommodation made for you in this class, please see me immediately.

Course Outline

  1. Introduction
    1. Demands for risk management tools
    2. Types of risk
  2. Tools
    1. The Matlab computer language
      Danielson, appendix C
    2. Statistical tools and the financial bootstrap toolbox:
      1. Probability basics
      2. Sampling, monte-carlo, and bootstrapping
      3. Hypothesis tests
      4. Time series
        Danielson, appendix A
  3. Financial data review
    1. Financial data reminder/review
      Danielson, 1.1-1.2
    2. Stylized facts of financial data
      Danielson, 1.3-1.7
  4. VaR analytics
    Danielson, 4.1-4.4
    1. Basics and interpretations
    2. VaR issues
    3. Expected shortfall
      Danielson, 4.5
  5. Estimating VaR
    Danielson, 5.1-5.3, 7.1,7.3.1
    1. Parametric methods
    2. Historical VaR
    3. Computational methods and precision
    4. Method comparisons
      Finger, How historical simulation made me lazy, Research Monthly, Riskmetrics, April 2006.
    5. Time aggregation and longer horizons
      Danielson, 4.6, 5.4
      LeBaron, Searching for lost decades, 2010.
    6. Extreme value theory
      Danielson, 9
  6. Volatility forecasting
    1. Modeling volatility
      Danielson, 2.1-2.3, 2.7-2.8
    2. Using volatility forecasts
      Danielson, 5.5
      1. Basic empirical conditional volatility
      2. Implied volatility and VIX
      3. High/low range information and realized volatility
  7. Correlations and portfolios
    1. Correlations and portfolios
      Danielson, 7.4
    2. Copulas
      Danielson, 1.8
    3. Very optional: multivariate volatility models
      Danielson, 3
  8. Fixed income and simple options
    Danielson, 7.2-7.3, light skim 6
    1. Bond and option pricing with simulation
    2. Options and partial risk hedges
  9. Applications and examples
    1. Bond swaps
      Case: Orange county: Marthinsen, chapter 6
    2. Exotic options and path dependence
    3. Pairs trading
  10. Default risk
    1. Measuring default risk
    2. Structured products
    3. Case: The Gaussian Copula and residential mortgages
      Hull and White, The risk of tranches created from residential mortgages, Financial Analysts Journal, 66, No. 5, 2010.
      Salmon, F., Recipe for disaster: The formula that killed Wall Street. Wired Magazine (February 23), 2009.
  11. Backtesting/stress testing
    Danielson, 8
  12. More risks
    1. Operational risk
      Case: Barings Bank: Marthinsen, 7
    2. Liquidity risk
      Background: Hedge Funds
      Case: LTCM : Marthinsen, 8
      Case: Amaranth: Marthinsen, 9
    3. Adjusting VaR for systemic risk: CoVaR
      Adrian and Brunnermeier, CoVaR, Princeton University, 2009.
  13. Risk and regulation: Summary, dangers, and crisis perspectives
    1. Danielson, 10
    2. Danielson et al., Endogenous risk, London School of Economics, 2011.
    3. Hull, The credit crunch of 2007: What went wrong? Why? What lessons can be learned?, University of Toronto, 2009.
    4. Campbell, The risk of value-at-risk, Risk, vol 22(4), 42-46.