Esoteric
Pendle PT Tokens as Zero-Coupon Bonds
Pendle PT as zero-coupon bond, YT as the floating leg of an interest rate swap.
TradFi →ZCB + interest rate swap
Prerequisites
01 · Concept — what problem does it solve?
The TradFi fixed-income toolkit, rebuilt on-chain. Every Pendle instrument maps exactly to a classic rate product:
- ≡ : buy below par, redeem at par at maturity, no coupons in between. The discount is the yield. A PT-stETH at 0.96 maturing in 6 months is a 6-month zero yielding ~8.4% annualized.
- ≡ receive-floating leg of an : pay fixed up front (the YT price), receive the floating yield stream until maturity. Profitable iff realized yield exceeds at purchase.
- PT + YT ≡ the underlying: the swap decomposition identity — par = principal leg + interest leg.
02 · Mechanics
- Discounting: PT trades at the present value of par under the market's implied rate; the quote ↔ implied APY are the same number in two units.
- Convergence: PT price grinds deterministically toward 1.0 at maturity ("pull to par") regardless of rate moves in between.
- Carry trade view: long YT = long realized-vs-implied yield ; long PT = short it (plus the fixed rate).
03 · Formulas
// zero-coupon pricing (t years to maturity)
P_PT = 1 / (1 + r)ᵗ
r = (1/P_PT)^(1/t) − 1 implied APY
// duration — rate sensitivity
D ≈ t (zeros: duration = maturity)
ΔP/P ≈ −D · Δr
// YT breakeven
realized_yield(t→T) ≷ P_YT paid
r=5%: PT starts at 0.9524 · r=10%: PT starts at 0.9091 · r=20%: PT starts at 0.8333 — all converge to 1.00 at maturity (pull-to-par).
04 · Edge cases & risks
- risk is real — long-dated PTs swing hard when implied yields reprice (e.g., points-meta hype inflating then deflating implied APYs).
- The DeFi — plotting implied APY across Pendle maturities gives a true on-chain term structure; it inverts when near-term yield hype exceeds long-run expectations.
- Credit ≠ risk-free — TradFi zeros discount against a risk-free curve; PT discounts embed smart-contract and underlying-protocol risk premia.