FE680 Advanced Derivatives



Course Catalog Description

Introduction

This course will address the practical and theoretical issues for interest rate models, credit models, and hybrid instruments. In the first part of the course, we will discuss the methodology and principles behind Interest rate models: Hull-White, HJM, Markovian HJM models. Mortgage derivatives and prepayment models will be discussed as an application of the interest rates models. The second part of the course will be focused on credit models: Default event and survival probabilities. Risk neutral and realized default probabilities, CDS, CDO, Gaussian copula model, base correlation and CVA. Hybrid Securities will be introduced and modeling issues will be discussed.

Prerequisite:

  • FE 620 – Pricing and Hedging

Campus Fall Spring Summer
On Campus X X
Web Campus X X X

Instructors

Professor Email Office
Dragos Bozdog
dbozdog@stevens.edu Babbio 429A
Hongkai Cao - Teaching Assistant hcao2@stevens.edu

More Information

Course Description

This course will address practical and theoretical issues for interest rate models, credit models, and hybrid instruments.

Prerequisites: Background in probability and applied mathematics


Course Outcomes

At the end of this course, students will be able to:

In the first part of the course we will discuss the methodology and principles behind Interest rate models: Hull White , HJM, Markovian HJM models. Mortgage derivatives and prepayment models will be discussed as an application of the interest rates models.

The second part of the course will be focused on credit models: building discount curves for credit models estimation of default probability and credit spread from equity prices. We will discuss Gaussian copula model, base correlation and CVA. Hybrid Securities will be introduced and modeling issues will be discussed.


Course Resources

Textbook

Damiano Brigo, Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer Finance(ISBN 978-3662517437)

Dominic O'Kane, Modelling Single-name and Multi-name Credit Derivatives, Wiley (ISBN: 978-0-470-51928-8))

Additional References

John Hull. Options, Futures, and Other Derivatives. 10th Edition. Pearson. (ISBN: 978-0134472089)

Lixin Wu, Interest Rate Modeling: Theory and Practice, Chapman and Hall/CRC Financial Mathematics Series, 1st Edition. (ISBN: 978-1420090567)

Jan De Spiegeleer, Wim Schoutens, Cynthia Van Hulle, The Handbook of Hybrid Securities: Convertible Bonds, CoCo Bonds and Bail-In, Wiley (ISBN: 978-1-118-44999-8)


Grading

Grading Policies

Assignments 60%

Final 40%

Graduate Student Code of Academic Integrity:

  • All Stevens, graduate students promise to be fully truthful and avoid dishonesty, fraud, misrepresentation, and deceit of any type in relation to their academic work. A student’s submission of work for academic credit indicates that the work is the student's own. All outside assistance must be acknowledged. Any student who violates this code or who knowingly assists another student in violating this code shall be subject to discipline.
  • All graduate students are bound to the Graduate Student Code of Academic Integrity by enrollment in graduate coursework at Stevens. It is the responsibility of each graduate student to understand and adhere to the Graduate Student Code of Academic Integrity. More information including types of violations, the process for handling perceived violations, and types of sanctions can be found at www.stevens.edu/provost/graduate- academics.

Lecture Outline

Topic Reading
Week 1 Static curves: Construction of discount factors, zero coupon rates, forward rates. Pricing bonds and interest rates swaps. Bond price sensitivity to interest rates moves (duration, DV01, convexity). Bootstrapping Yield Curve.
Week 2 Interest Rate Derivatives (Convexity, Timing, Quanto Adjustment)
Week 3 Interest Rate Derivatives: The Standard Market Model
Week 4 Interest Rate Derivatives: Models of the Short Rate
Week 5 Interest Rate Derivatives: HJM and LMM
Week 6 Swaps Revisited
Week 7 Credit models: Default event and survival probabilities. Risk neutral and realized default probabilities. Cash flows conditional on default and survival probabilities. Forward default intensity curve. Pricing credit default swaps. Survival probability and recovery values.
Week 8 CDS. Implied hazard rates. Implied default curves.
Week 9 CDO’s: Introduction, Gaussian copula models, Large portfolio Approximation
Week 10 Base Correlation framework ; Merton’s Asset Value Model
Week 11 Modelling Default Times using Copulas
Week 12 No Class (Thanksgiving Recess).
Week 13 Statistical Inference for Copulas (MLE, IFM, CML, Empirical)
Week 14 Hybrid Securities: Convertible Bonds, CoCo Bonds and Bail-In