This is the capstone. Seven lessons built the fixed-income engine from one honest promise outward — price a bond by discounting its cash flows; measure its rate sensitivity as a time, a percentage, and a dollar-per-basis-point; correct duration’s straight-line lie with convexity; strip coupon bonds into a spot curve and extract the forwards it hides; watch the short rate revert to a mean in Vasicek and CIR; split a risky yield into expected loss and risk premium; and defend a whole balance sheet by matching duration and sizing a DV01 hedge. No formula sheet, no hints, no take-backs: every answer locks the instant you submit, the wrong options are the exact traps that catch real rates traders, and your score stays hidden until the end.
How this exam works
This is a graded exam. Questions arrive one at a time. Once you submit an answer it is final — there is no going back, no second try, and a wrong answer simply fails that question. Your score stays hidden until the very end, where you need 70% to pass. Read every option before you commit.
A bond's price is fundamentally equal to:
Select an answer to continue.
Whatever the score reads, the chain you just stress-tested — pricing, duration, convexity, the bootstrapped curve, forwards and term-structure models, credit spreads, and immunization — is the literacy every rates trader, fixed-income PM, and risk manager leans on. Here is the entire topic in one glance.
Big picture
The Fixed-Income Analytics Toolkit
- Fixed-Income Analytics
- Bond pricing
- Price = PV of cash flows at the yield
- YTM = the IRR that prices the bond
- Coupon vs yield → premium/par/discount
- Dirty = clean + accrued
- Duration
- Macaulay: PV-weighted average time (years)
- Modified: ΔP/P ≈ −D·Δy (% per yield)
- DV01 = D·P·0.0001 (dollars per bp)
- Maturity ↑, coupon ↓, yield ↓ → duration ↑
- Convexity
- Second-order: + ½·C·(Δy)²
- Always favours the holder
- Barbell out-convexes a bullet
- Callables/MBS → negative convexity
- The curve
- Bootstrap spots from coupon bonds
- Short end first, one unknown per step
- Forwards bridge two spots (no-arbitrage)
- Inverted curve → recession signal
- Term-structure models
- Short rate r_t, mean-reverting
- Vasicek: constant vol, can go negative
- CIR: σ√r vol, floored at zero
- One-factor → limited curve shapes
- Credit risk
- Spread = risky − risk-free yield
- s ≈ PD × LGD + risk premium
- LGD = 1 − recovery (seniority matters)
- Model cracks in correlated crises
- Immunize & hedge
- Match duration (and convexity) to liabilities
- DV01 hedge: N = −DV01_book / DV01_hedge
- Twist risk → key-rate durations
- Spread risk needs its own hedge
- Bond pricing