Enter par yields by year and Quantora bootstraps the zero-coupon (spot) and implied forward curves, then derives the par swap rate, PV01, and a bond's Z-spread. This is the foundational rates primitive - every consistent bond and swap valuation discounts off a zero curve, not off par yields.
Par yield curve (annual, %)
Editable. Defaults approximate a normal upward-sloping curve; type your own to reprice everything live.
Curves
Par (input) vs bootstrapped zero (spot) vs implied 1-year forward rates.
Par yieldZero / spotForward (1y)
Z-spread solver
Constant spread over the zero curve that reprices a fixed-coupon bond (annual coupons, face 100) to its market price.
A par yield is the coupon rate at which a bond trades at 100. But cashflows at different dates deserve different discount rates - the zero (spot) curve - which we recover by bootstrapping: solve each maturity so its par bond reprices to 100, working outward. Forward rates are the future short rates the curve implies (a steep curve implies rising forwards). The par swap rate is the fixed rate that makes a fixed-for-floating swap worth zero at inception, and PV01 is the value change per basis point of the fixed rate. A bond's Z-spread is the parallel shift to the entire zero curve that matches its market price - a cleaner richness/cheapness measure than yield-to-maturity because it respects the curve's shape.
Bootstrap assumes annual-coupon par bonds priced at 100 on consecutive yearly tenors; single-curve swap valuation (float leg par at reset). Educational analytics, not a pricing source or investment advice. Math from Quantora's verified engine library.