This course teaches the valuation of fixed-income and credit products. It starts from signed cash flows, rates, and discounting. It then values fixed-rate bonds, forwards, and European options, and it ends with options on a bond and with credit default swaps (CDS). The seven parts build on each other, and each part states which earlier parts it uses.
The chapters work in toy models. A toy model has stated inputs, and the chapter states what the model simplifies or leaves out. A chapter states what you will be able to do, explains the idea before the formula, and works a numerical example. Most chapters end with a knowledge check and a model boundary. Some chapters add an interactive lab, in which you change the inputs and see the result change.
The course is an educational draft. It is not a pricing system, and it uses no live market data.
Every part is a starting point. Start at Part 1 if the course is new to you. The two learning paths go through the course in a fixed order. Both paths assume only basic algebra, percentages and decimal notation, and integer exponents, and both begin with the same chapter: Cash-flow timelines and perspective.
Credit products path
From discounting to the value and the market quote of a CDS.
Bond derivatives path
From discounting to options on a bond, including an option that issuer default extinguishes.
To start at a later part, first read the parts that it requires, and the parts that those parts require. The curriculum map shows the same requirements chapter by chapter.
Each part opens with an overview page that states what the part covers, how it builds on the earlier parts, and the argument that runs through its chapters. Equations, tables, diagrams, knowledge checks, and worked examples are numbered by part and chapter, and each kind starts again in every chapter, so equation (1.5.1) is the first numbered equation of the fifth chapter of Part 1. Section headings are numbered the same way.
Part 1 · 7 chapters
Place signed payments on one time axis before valuing them.
Calculate expected values from disjoint events, including values that vary inside an event.
Separate an annualized quote from its periodic rate and its units.
Convert one deterministic future unit into its value at time zero.
Discount each signed dated amount and then add the comparable values.
Match every dated state-contingent cash flow before using one portfolio to value another.
Separate real-world forecasts from no-arbitrage pricing weights, then discount a finite-state expected payoff.
Part 2 · 6 chapters
Translate face value, coupon rate, frequency, and maturity into promised payments.
Apply one discount factor to each promised payment before adding.
Interpret the rate that reproduces a toy bond price, then calculate the price from an input yield.
Explain why the price of fixed positive cash flows decreases when the yield increases, and why the price-yield curve is not linear.
Calculate actual/actual coupon-period accrual and keep quoted and cash bond prices on one basis.
Apply cash-and-carry to a coupon bond while keeping coupon ownership and dirty-price units explicit.
Part 3 · 1 chapter
Move from one discount factor to a dated deterministic curve and derive future-to-future discount factors.
Part 4 · 5 chapters
Separate a forward's obligation, fair delivery price, and changing signed contract value.
Separate call and put rights from expiry payoff, current value, premium, and profit.
Match European call and put portfolios state by state before solving a missing value.
Price two-state option payoffs by both exact replication and risk-neutral weighting.
Extend one-period risk-neutral valuation to node-by-node backward induction with local discount factors.
Part 5 · 2 chapters
Define a standalone option on a bond, put its prices on one cash-price basis, and value expiry payoffs on an input lattice.
Value a bond option that is extinguished by issuer default while keeping bond recovery separate.
Part 6 · 2 chapters
Read an input survival curve, calculate interval default probabilities, and use a constant-hazard toy model.
Value a narrowly defined recovery-of-par claim whose survival and default-state payments both occur at maturity.
Part 7 · 4 chapters
Build exact default-time expectations for the two CDS legs and solve the zero-upfront par spread.
Distinguish a conventional CDS spread quote from a fixed running coupon, identify which quantity is observed and which is solved, calculate the signed upfront amount, and reverse the simplified conversion.
Separate what the CDS market shows from what a pricing model assumes or solves, read a credit curve as tenor marks plus a fitted survival curve, and distinguish transforming quotes from fitting the curve.
Measure a CDS position's sensitivity to the liquid tenor's quote by bump and reprice, then size the liquid-tenor equivalent notional and equivalent ratio that offset it.
Prerequisite-aware
Each chapter declares the exact competencies that it requires and teaches. A validator rejects a missing reference and a cycle.
One meaning per symbol
Each symbol in the rendered math resolves to one notation entry. The notation glossary collects the shared entries.
Tested numbers
Each worked number comes from the course’s tested calculation code or from a cited source. The models state their units, signs, and conventions.
Draft until reviewed
The material was drafted with AI assistance. Each chapter stays marked draft until a person checks its prose, sources, formulas, and numbers.
Educational use only. This site is not investment, legal, tax, accounting, valuation, or trading advice.