Bootstrap zero rates from par yields calculator

Where discount factors actually come from.

Interactive: bootstrap zero rates from par yieldsHard

Four annual par yields in; four zero rates, a discount factor and a forward out.

1-year par yield % 2-year par yield % 3-year par yield % 4-year par yield %

1-year zero: —
2-year zero: —
3-year zero: —
4-year zero: —
4-year discount factor: —
Implied 3y→4y forward: —

Note what an upward-sloping par curve does: every zero rate sits above its par yield, and the forwards sit above both. That is not a forecast of rising rates — it is arithmetic. Flatten the four inputs to the same number and watch zeros, par yields and forwards collapse onto each other.

The idea behind it

This calculator belongs to Curve Construction & Bond Math, where the mechanism it computes is explained step by step, with the formula, what each input means and where the simple model stops being right. Everything is computed in your browser; nothing you type is sent anywhere.

Instruments it applies to

Zero-Coupon Bond — No coupons, one payment: buy at a discount, collect face value at maturity. The purest interest-rate instrument.

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Not advice. This explains how something works; it is not a recommendation, and nothing here is tailored to you. You can lose everything you put in — with leveraged instruments, considerably more. StrikeAndYield is not a regulated firm and provides no financial services.

The same in full — six points, and why each one matters

No advice, no recommendation. Nothing on this page constitutes investment, financial, legal, tax or accounting advice, a personal recommendation, or an offer or solicitation to buy or sell any financial instrument.
Nothing here is tailored to you. This is written for a general audience. It does not consider your objectives, financial situation, knowledge, time horizon or tolerance for loss.
The examples are simplified. Worked examples use round numbers and leave out costs, spreads, taxes, collateral, settlement and market conventions that materially change real outcomes.
The models are teaching models. Formulas shown are standard textbook formulations. Institutions add calibration, live market data and credit, funding and capital adjustments — nothing here will reproduce a dealer’s quote or produce a valuation you can rely on.
These instruments carry risk. You can lose your entire investment. Leveraged instruments — futures, options, CFDs, perpetual futures and similar — can cost you considerably more than you originally deposited.
We are not a regulated firm. StrikeAndYield is an independent publication by DELISORIA. It is not a bank, broker, fund manager or licensed adviser, it provides no financial services, and reading it creates no client relationship. For decisions about your own money, consult a professional licensed in your jurisdiction. See the full disclaimer.