# FE 535 Introduction to Financial Risk Management: Financial Engineering and Statistical Analysis

Professor: Dr. Rupak Chatterjee, Citi Global Markets

Office: Babbio 5^{th} Floor

Email: Rupak.Chatterjee@stevens.edu

Class Schedule: Tuesdays 6:15 p.m. to 8:45 p.m., Babbio 122

Hanlon Lab: Aug 30th, Sept 6th, Sept 13th Friday 5:00 p.m. – 7:00 p.m (Bloomberg Training)

Office Hours: Wednesday 3:00 p.m. to 5:00 p.m.

## Contents |

## Course Objectives and Description

Risk Control and derivative pricing are major concerns for financial institutions. Yet, as recent events have shown us there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial market. Many of the standard models seen on Wall Street however are based on simplified assumptions and can lead to systematic (and sometimes dramatic) underestimation of real risks. Starting from a detailed analysis of market data, one can take into account more faithfully the real behavior of financial markets (in particular the ‘rare events’) for asset allocation, derivative pricing and hedging, and risk control. This course will introduce some concepts to better address these issues. As these ideas are not (yet) standard, they are not found in any one book and the course will largely be based on lecture notes. There will also be two sessions in the Hanlon lab learning to use a Bloomberg terminal.

Various financial instruments will be presented in a form familiar to Wall Street traders (i.e. Bloomberg screens). The purpose of Risk Management is to provide a valuation of these financial contracts ("pricing") and to provide various measures of risk and methods to hedge these risks as best as possible ("hedging"). These tasks are not just performed by "Risk Managers" but by "Traders" who price and hedge their respective trading books on a daily basis. Successful trading (over extended periods of time) comes down to successful risk management. Successful risk management comes down to robust valuation which is the main prerogative of Financial Engineering. Valuation of financial instruments begins with an analysis of possible future events (i.e. stock price moves, interest rate moves, defaults, etc.). Dealing with the future involves the mathematics of statistics and probability. The first step is to find a probability distribution that is suitable for the financial instrument at hand. The next step is to calibrate this distribution. The third step is to generate future events using this calibrated distribution and based on this, provide the necessary valuation and risk measures for the financial contract at hand. The failure of any of these steps can lead to incorrect valuation and therefore an incorrect assessment of the risks of the financial instrument under consideration.

## Course topics

- Financial Instruments: Bloomberg Analysis
- Statistical Analysis of Financial Data
- Stochastic Processes
- Statistical Modeling of Trading Strategies

## Textbook (uploaded to Moodle)

1. Modern Methods of Financial Engineering and Risk Management, Rupak Chatterjee, Apress-Springer, to be published, 2014.

## Some Useful References

- Risk Management and Financial Institutions, John Hull, John Wiley & Sons, 2012 (optional)
- An Introduction to the Mathematics of Financial Derivatives, 2nd Edition, Salih Neftci, Academic Press, 2000 (optional)
- Monte Carlo Methods in Financial Engineering, Paul Glasserman, Springer-Verlag, 2004 (optional)

### Syllabus

Chapters from Lecture notes: Modern Methods of Financial Engineering and Risk Management:

1 Financial Instruments 1

1.1 Bloomberg Screen: BTMM- US Treasury & Money markets

1.2 Bloomberg Screen: USSW- US Govt/Swap/Agency Composite

- 1.2.1 Options Terminology

- 1.2.2 Homework: Create a Black Formula Implied Volatility Calculator

- 1.2.3 Caps and Floors

- 1.2.4 Swaptions

2 Building a Yield Curve 31

2.1 What are they used for?

2.2 Overview of Construction

2.3 Cash Libor rates

2.4 3MEurodollar Futures

2.5 Swaps

2.6 Generic Discount Factors

2.7 Homework: Build a Simple Yield

3 Statistical Analysis of Financial Data 39

3.1 Tools in Probability Theory

3.2 Analysis of Financial Data

- 3.2.1 Homework: Create a Gaussian Random Number Generator in Excel

- 3.2.2 Homework: Create a Mixture of Gaussians in Excel

3.3 Analysis of Financial Data: Moment Matching

- 3.3.1 Homework: Calibrate S&P 500 Returns to a Mixed Normal in Excel

- 3.3.2 Homework: Calibrate SX5E Returns to a Student t-distribution in Excel

- 3.3.3 Homework: Create a Skew Normal Distribution in Excel

3.4 Analysis of Financial Data: Risk Measures

- 3.4.1 Homework: VAR and CVAR

3.5 Tools in Probability Theory: Term Structure of Statistics

- 3.5.1 Homework: Term Structure of Statistics

3.6 Tools in Probability Theory: Joint Distributions

- 3.6.1 Homework: Joint Distributions

3.7 Analysis of Financial Data: Dynamic Portfolio Allocation

- 3.7.1 Homework: Dynamic Portfolio Allocation: EEM versus EEMDPA

3.8 Tools in Probability Theory: Correlation Limits Portfolio Diversification

4 Stochastic Processes 93

4.1 Definitions

4.2 Examples

4.3 Brownian Motion Process for Stock Returns

4.4 Monte Carlo Simulation

- 4.4.1 Homework: Brownian Motion Process for Stock Returns

- 4.4.2 Homework: Ito’s Lemma

4.5 GARCH Process for Stock Returns

- 4.5.1 GARCH(1,1): "Traditional" Term Structure of Volatility

- 4.5.2 Homework: Calibrate a GARCH(1,1) Process for SX5E

- 4.5.3 Homework: Create a GARCH(1,1) Simulator in Excel

4.6 Statistical Modeling of Trading Strategies

- 4.6.1 Example [Stat Arb] Strategy

- 4.6.2 Homework: MCD versus

- 4.6.3 Homework: Calculate daily S-scores for MCD vs XLY

4.7 Appendix: Definitions

4.8 Appendix: Examples of Ito’s Lemma

4.9 Appendix: Black Scholes with Holes

## IT Requirements

All the homeworks require the use of Excel with the following properties:

- 1) Functions:
- a.Offset()
- b.Rand()
- c.Norminv()
- d.Skew(), Kurt(), Average(), Stdev()
- e.Gammaln()

- 2) Data Analysis Function : Histogram

**Attention Apple Users:** Even though you may have Excel, the above functionality does not come with all Apple versions of Excel so you better check to see what your Excel provides.

Week | Topic(s) | Homework |
---|---|---|

1 | Financial Instruments | |

2 | Financial Instruments | |

3 | Financial Instruments | Problem 2.1: Building a LIBOR Yield Curve |

4 | Financial Instruments | Problem 1.1: Black Formula Calculator and Implied Volatility |

5 | Statistical Analysis of Financial Data | Problems 3.1-3.2: Inverse Transform Method / Mixed Gaussians (method one and two) |

6 | Statistical Analysis of Financial Data | Problems 3.3-3.4: Calibrate S&P returns to a Mixed Gaussian, SX5E to Student t-dist |

7 | Statistical Analysis of Financial Data | Problems 3.5: Create a Skew Normal Dist Problems 3.6: VAR/CVAR |

8 | Monday Schedule | |

9 | Statistical Analysis of Financial Data | Problems 3.7: Term Structure of Skew, Kurt, Up & Down Volatility |

11 | Midterm | |

12 | Introduction to Stochastic Processes | HWK 4.1: Brownian Motion MC Simulator |

13 | Introduction to Stochastic Processes | HWK 4.2: Ito’s Lemma |

14 | Statistical Arbitrage | HWK 4.3: GARCH(1,1) |

15 | Statistical Arbitrage | HWK 4.5: Pairs Trading |

16 | Statistical Arbitrage and Review | |

17 | Final Exam(In Class) |