Zero-coupon rate
Definition · Level 11 · Pricing toolkit
Keep reading with Tradecraft
Without a subscription, you can read three definitions every 30 days. Tradecraft explains all 988 terms and strategies, with the lessons that teach them, flashcards that come back before you forget, quizzes and a payoff lab.
The yearly rate on money lent from today to date T and repaid in one payment at T, with no coupons in between; also called the zero rate. It converts to a discount factor: 1/(1 + z)^T.
Example
A 2-year promise of 100 costs 92.46 → the zero rate is (100 ÷ 92.46)^(1/2) − 1 = 4.00%.
Where Tradecraft teaches it
Level 11 · Pricing toolkit, in the lesson “Discount factors & forward rates”: The price today of a promise of money later, a bond as a bundle of such promises, and the forward rates hidden in today’s rates.
Related terms
- Discount factorToday’s price of 1 paid at date T: 1/(1 + z)^T or e^(−zT).
- Forward rateThe rate for a future period that today’s curve locks in: (1 + z₂)² = (1 + z₁)(1 + f).
- 0.4 ruleAt-the-money-forward call or put ≈ 0.4 × S × σ × √T (small dividends, modest σ√T), because 1/√(2π) ≈ 0.4.
- Arbitrage boundsPrice limits any option must respect, or someone locks in a riskless profit: call ≤ S, European put ≤ K·e^(−rT), call ≥ max(0, S − K·e^(−rT))…
- Backward induction (pricing tree)Solving a problem from the last step back to the first.
- Binomial risk-neutral probabilityThe up-move weight q = (1 + r − d)/(u − d) that makes the stock earn the risk-free rate in a one-step tree; the option is the discounted q-weighted…