A. Course description
The course objective is to introduce students to mathematical modeling, pricing and trading strategies for credit instruments.
The course will cover:
- corporate and sovereign bonds
- credit default swaps (CDS) and credit default indices (CDX),
- fixed income ETFs,
- collateralized debt obligations (CDOs),
- mortgage and municipal bonds.
Real market data examples will be used for pricing and risk management.
The students will have the opportunity to discuss various trading strategies with market practitioners, for a better insight into the "daily activity" of credit trading desks.
B. Prerequisites
Undergraduate-level calculus, linear algebra, and probability. Familiarity with fixed income financial instruments, in particular US Treasuries, SOFR swaps/futures. Intermediate programming knowledge in Python. Some familiarity with Bloomberg terminals would be a plus.
C. Grading
50% homework
40% final exam
10% participation
D. Final Exam
The final exam will take place on Tuesday May 27 2025 in the same location as the class - MS 112.
The exam will start at 12:30pm and finish at 3:15pm, for a total of 2h 45 mins.
It will cover programming as well as conceptual & math questions.
E. Course outline
Session 1 (Cash Instruments)
Quick introduction to history of credit markets
What is credit default risk?
Overview of cash credit instruments: corporate bonds and loans
Market segments / role of credit rating agencies
Fixed vs floating rate coupons, contractual cashflows, seniority ranks, credit events
Coupon accrual, “dirty” vs. “clean” prices, settlement dates
Quoting conventions: prices, yields and spreads to benchmarks / “YAS screen” in Bloomberg
Embedded optionality in callable bonds: computation of workout dates
Valuation and risk management: DV01, duration, carry, curve rolldown, convexity, jump-to-default
Trading details: OTC vs. electronic venues, average volumes, TRACE reporting facility
Session 2 (Derivative/Synthetic Instruments)
Sovereign bonds
Corporate bond indices and credit ETFs (LQD, HYG, EMB)
Financed floating rate bonds
Overview of synthetic instruments: credit default swaps, CDX IG/HY credit indexes
CDS as a portfolio hedge against issuer credit defaults
CDX as macro trading product
Role of ISDA committee: determining default event, recovery rate auctions
Quoting conventions: price upfronts, quoted spreads, par spreads, index rolls
ISDA standard pricing model / “CDSW screen” in Bloomberg
Session 3 (Pricing and Risk Analytics)
QuantLib as pricing and risk analytics library
Overview of Python example notebooks
Understanding pricing for:
- generic (fixed & floating rate) cashflows
- risk-free government bonds
- IR swaps (SOFR)
- SOFR and Fed Funds futures
- risky corporate bonds
- fixed income ETFs
Risk-free curve calibration (bootstrapping) using:
- US cash (on-the-run) treasuries
- SOFR swaps/futures
- Fed Fund futures
- cash Bunds (EUR curve)
Risk management: duration, convexity and bucketed IR risks
Session 4 (The Hazard Rate Model)
Pricing generic credit instruments using the hazard rate model
Bootstrapping survival probability and hazard rate curves
Issuer credit curve shapes and the connection to the credit cycle
CDS pricing in the hazard rate model
ISDA CDS standard pricing model
CDX IG/HY valuation and risks
Risky bond pricing in the hazard rate model
Derivation of price sensitivites: IR01, CS01, REC01, JTD
Yield/spread vs. hazard rate models
Session 5 (Curve Shape Models)
Historical PCA analysis of bond yield curves
Parametric yield curves: Nelson-Siegel model and extensions
Smooth credit curve models
Issuer curve calibration in hazard rate space
Interpreting model results: edges and alpha signals
Quantitative trading in credit markets
Managing risks: credit spread, interest rates, “jump-to-default”, funding
Portfolio construction and trade execution
Strategy backtesting
Trading strategy examples
Session 6 (Trading Insights with Market Practitioners)
David Hermann, senior portfolio manager
Dan Wang, senior quantitative researcher
Insights into daily activity of a credit trading desk
Overview of various credit instruments and trading strategies
Fundamental vs Quantitative approach to trading
Q&A session on recent events in US investment grade credit markets
Session 7 (Structural Credit Models)
Structural approach to credit default risk
Structural credit models: the Merton model
Fair value of equity
Fair value of risky bonds
Leverage effect and equity volatility smiles
Capital structure strategies
Session 8 (Correlated Defaults and CDOs)
Correlated Defaults in the Merton model
Modeling credit losses in pools of risky instruments
Loss distributions for general (non-homogeneous) pools
Collateralized Debt Obligations
CDO tranches and structural subordination waterfalls
Synthetic CDO Pricing / CDX IG Index tranches
Base Correlation model and CDO quoting conventions
CDOs in the 2008 financial crisis
Session 9 (Mortgage and Municipal Bonds)
Mortgage Backed Securities (MBS)
Origination, pooling, securitization, issuance, and trading
Pricing and risk management
Role of GSEs and government agencies
Impact of credit rating agencies
Collateralized Mortgage Obligations (CMOs)
Mortgage Backed Securities in the 2008 financial crisis
Municipal bonds: specs, pricing, credit risk and tax benefits
Building smooth credit curve models for municipal bonds
Investing in municipal bonds via ETFs