Module 23 · Advanced
Credit risk — and how it's computed
Credit riskis the risk that a borrower doesn't pay you back — that a bond, loan or counterparty defaults, or that the market's perception of that chance (the credit spread) moves against you before it does. It's the dominant risk in most of fixed income, and remarkably, every credit instrument — a plain bond, a convertible, a credit default swap — is measured with the same handful of numbers.
The five numbers behind all of it
- PD — probability of default. How likely the borrower fails to pay, over a horizon. It comes from ratings, from a structural model, or — most directly — from the credit spread itself via the credit triangle: hazard λ ≈ spread ÷ (1 − recovery). From λ, survival is e^(−λt) and cumulative default is 1 − e^(−λt).
- LGD — loss given default. How much you actually lose if it happens: 1 − recovery rate. Senior secured might recover 60–70%; subordinated or equity, far less.
- EAD — exposure at default. How much is on the line — the notional, or for a derivative the expected positive exposure (from Module 14).
- Expected loss. The average you'd lose, priced into every yield: EL = PD × LGD × EAD.
- Unexpected loss & the two sensitivities. Beyond the average, you carry spread risk (CS01) — P&L per 1bp of spread widening — and jump-to-default (JTD) — the instant loss if the name defaults outright. CS01 is the slow bleed; JTD is the cliff.
What changes across instruments is where those numbers live. Flip between the three tabs below and watch the same engine reshape itself.
🎛 Credit-risk calculator
λ (hazard) = spread / (1−R) = 300bp / 0.60 = 5.00% PD(t) = 1 − e^(−λt) survival = e^(−λt) CS01 = spr.dur × MV × 1bp JTD = MV − Recovery × notional EL = cumPD × LGD × notional
PD 1yr
4.88%
cum PD 5y
22.1%
CS01
$4,158
per +1bp
Jump-to-default
-$5,900,000
loss if default now
Expected loss 5y
$1,327,195
Market value
$9,900,000
Every credit instrument reduces to the same three numbers — PD (how likely default is), LGD = 1−recovery(how much you lose if it happens), and exposure — plus how the value moves with the spread (CS01) and the jump if it defaults outright (JTD). Educational tool — not investment advice.
① Corporate bonds — credit risk in its purest form
You own the whole credit exposure directly. Back out the hazard rate from the spread, and you have the default curve, the CS01 (spread duration × market value × 1bp) for the day-to-day spread risk, and the JTD (market value − recovery × notional) for the cliff. Expected lossis cumulative PD × LGD × notional. Widen the spread and every one of these grows together.
② Convertibles — credit risk hiding under an equity option
A convertible is a bond you can swap for shares, so it's two things at once: a bond floor (a normal credit-risky bond — coupons and face discounted at the risk-free rate plus the credit spread) and a conversion option on the stock. The credit risk lives entirely in that bond floor.
The twist is how much credit risk you have depends on the share price. When the stock is high the convert trades like equity (delta near the full conversion ratio, credit almost irrelevant). When the stock falls far below the conversion price the option is worthless and the convert becomes a “busted convertible”— a pure distressed bond, where credit risk and JTD dominate. On default you're left with recovery × face and the option is zero. The chart shows the convert riding above the bond floor and parity — slide the stock down and watch it collapse onto the floor, where credit takes over.
③ Credit derivatives — credit risk as a standalone trade
A CDS strips credit risk out of the bond and lets you trade it on its own. Value is the risky annuity times the spread difference: MtM = side × (spread_now − spread_contract) × RPV01 × notional. Its CS01 is RPV01 × notional × 1bp. But the number that defines a credit derivative is JTD: buying protection means on default you collect LGD × notional(a gain), while selling protection means you pay it (a loss). So a protection buyer is short credit — positive JTD, profits as spreads widen — and the seller is long. Index and tranche products add default correlationas a further risk factor (see the CLO module).
Things to try
- • On the bond tab, widen the spread from 300 to 800bp — hazard, PD, CS01 and JTD all jump, and the default curve steepens.
- • On the convertible tab, drag the stock down — watch the regime flip to busted (credit) as the convert falls onto its bond floor and credit DV01 takes over from equity delta.
- • On the CDS tab, switch between buy/sell protection — the JTD flips sign: the same default is a windfall for one side and a hit for the other.
- • Move recovery for any instrument — it changes LGD, and therefore both the hazard implied by the spread and the size of the jump.