Researcher course in fixed income
Credit Default Swaps, Copulas and Counterparty Risk
Credit default swaps from the contract to the model: what is protected and paid, hazard rates and survival curves, bootstrapping a CDS curve with the ISDA standard model, index products, and the basis between bonds and CDS. It also teaches copula models for portfolio credit risk and counterparty credit risk and CVA.
A credit default swap is insurance on a borrower’s debt, and its spread is the clearest market price of default risk. Banks use credit default swaps to hedge loans, funds use them to take views on companies and countries, and risk teams use their spreads in counterparty and capital models. This course covers the contract, the pricing model and the trades.
How is default turned into a price?
By treating default as a random time with an intensity, the hazard rate. From quoted spreads a desk bootstraps the probability that the company survives to each date, and from those probabilities it prices any credit instrument on that name. The course builds this curve step by step with the industry’s standard model.
How is the course taught?
Audio lessons give the general subject, explainer films show survival curves being built, and the workbooks hold worked pricing examples, notebooks and cheat sheets of market conventions. The curve lab receives written feedback from the faculty.
Where are copula models used today?
A copula describes how risks move together, separately from how each one behaves alone. In credit, that is the question that matters: one default is a loss, but many defaults at once is a crisis. This course teaches the copula models used for credit portfolios, CDO tranches and bank capital, and the limits that 2008 exposed.
In bank capital, where the one-factor Gaussian model underlies the Basel formula for credit risk; in credit portfolio management; in pricing index tranches; and in market risk wherever joint tail losses matter. Each unit works one of these on data.
Why is exposure the hard part?
Counterparty credit risk is the risk that the other side of a trade defaults while it owes you money. Every bank with a derivatives book measures it daily, prices it into each trade as a credit valuation adjustment, and holds capital against it. This course teaches the simulation, the adjustments and the rules.
Because what a counterparty will owe you in a year depends on where markets go. A bank therefore simulates thousands of market paths, values its whole book with that counterparty on each, applies netting and collateral, and only then knows its exposure. The course builds that engine for a small swap book.
Who is this course for?
Quants and analysts heading for credit trading, risk or model validation.
What you will be able to do
- Describe the CDS contract, credit events, auctions and the standard coupons and upfront payment.
- Bootstrap a survival curve from CDS quotes and price a CDS with the standard model.
- Measure credit spread and default risk, and hedge a bond with a CDS.
- Explain CDS indices, their tranches and the bond-CDS basis.
- Explain Sklar's theorem and build Gaussian, Student t and Archimedean copulas.
- Simulate expected and potential future exposure for a portfolio of swaps and options.
Syllabus, module by module
The contract
Protection buyer and seller, credit events, auctions, standard coupons and upfront.
Default as a random time
Hazard rates, survival probabilities and recovery.
Pricing a CDS
Premium and protection legs and the ISDA standard model.
The CDS curve
Bootstrapping survival curves and reading term structures of credit.
Dependence beyond correlation
Why linear correlation is not enough, rank correlation and tail dependence.
What counterparty risk is
Bilateral and cleared trades, default of a counterparty and replacement cost.
What every course contains
Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.
- Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
- Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
- Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
- Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
- Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
- Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
- Transcript. A full transcript of every film and every audio recording, searchable and quotable.
- Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
- Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
- Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.
How the certificate is earned
Graded problem sets and a final lab: bootstrap a CDS curve for a company and value a position in its bonds and CDS. On a pass you receive the Course certificate in Credit Default Swaps, Copulas and Counterparty Risk, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. Read how certification works.
Before you start
This course assumes the material of the courses below, or the same knowledge gained elsewhere.
This course counts toward
- Certificate in Quantitative Risk ManagementA financial risk management certification in six courses and a capstone on measuring and governing market and credit risk: VaR and expected shortfall, volatility models, stress tests, credit and counterparty risk, bank capital and the validation of the models themselves.
- Fellowship in Computational FinanceThe top credential on the researcher path. Twenty-one courses and a dissertation supervised in writing and examined by two faculty members.
Questions applicants ask
What is a credit default swap?
It is insurance against a borrower’s default. The buyer pays a regular premium; if the borrower defaults, the seller pays the loss on the debt. Its price, the CDS spread, is the market’s view of that borrower’s credit risk.
Is this course useful for risk roles?
Yes. Credit spreads feed counterparty risk, credit valuation adjustment and capital models. This course goes on to counterparty credit risk with CVA and to copula models for portfolio credit risk.
What is a copula in finance?
A copula is a function that joins the separate distributions of several variables into a joint distribution, so that the dependence between them can be modeled on its own. In credit it describes how defaults cluster.
What is CVA?
Credit valuation adjustment is the reduction in a derivative’s value for the chance that the counterparty defaults while owing you money. It is computed from simulated future exposure, the counterparty’s default probabilities and the expected recovery.