FE680 Advanced Derivatives
Course Catalog Description
Introduction
Prerequisite:
- FE 620 – Pricing and Hedging
Campus | Fall | Spring | Summer |
---|---|---|---|
On Campus | X | X | |
Web Campus | X | X | X |
Instructors
Professor | 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 |