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 430

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: bootstrapping the yield curve, interest rate derivatives, equilibrium and no‐arbitrage models of the short rate, numerical implementations.
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, multi‐ name latent variable model, copula models. Hybrid Securities will be introduced, and modeling issues will be discussed.

Course Resources

Textbook

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

2.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

		Weights
1	Class Participation	5%
2	Assignments	55%
3	Final	40%

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	Interpolation Methods (Linear, Exponential, Cubic Spline, Nelson‐Siegel Model). Interest Rate Derivatives (Bond Options).
Week 3	Interest Rate Derivatives (Caps and Floors, Swaptions). Convexity, Timing, Quanto Adjustment. Non‐Standard Swaps (Compounding Swaps, Currency Swaps, LIBOR‐in‐arrears swaps, CMS and SMT swaps, Differential Swaps).
Week 4	Interest Rate Derivatives: Models of the Short Rate. Equilibrium Models (Vasicek, CIR). No‐Arbitrage Models (Ho‐Lee, Hull‐White One‐Factor Model, Black‐Derman‐Toy Model, Black‐ Karasinski Model).
Week 5	Interest Rate Derivatives: Models of the Short Rate (Hull‐White: Two‐stage procedure for constructing trinomial trees, Vasicek Model: Recombining binomial tree procedure).
Week 6	Interest Rate Derivatives: (Hull‐White Two‐Factor Model, HJM Model, and BGM Model).
Week 7	Credit Risk: Default event and survival probabilities. Risk neutral and realized default probabilities. Forward default intensity curve. Estimating Default Probabilities using Bond Prices and Historical Data. Meton’s Model.
Week 8	CDS (CDS and Bond Yields, Valuation of Credit Default Swaps).
Week 9	Implied Hazard Rates from CDS spreads. Implied default curves.
Week 10	CDO (Cash and Synthetic CDO, Waterfall Mechanism, STCDO, Valuation of Tranches).
Week 11	Gaussian Latent Variable Model (CDO and Correlation, Multi‐Name Latent Variable Model, Asset Correlation and Dependency, Conditional Hazard Rates, Portfolio Loss Distribution, Simulating Multi‐Name Defaults).
Week 12	Modelling Default Times using Copulas (Default Times Dependencies, Measure of Dependency, Default and Survival Copula Functions: Gaussian, Student‐t, Marshall‐Olkin, Archimedean Copulas.
Week 13	Statistical Inference for Copulas (MLE, IFM, CML, Empirical).
Week 14	Review and Catch‐up. Hybrid Securities (Tentative).
Final Week	Final Exam