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This page covers the formulas that drive PT/YT pricing across Exponent. Developers don’t need to implement pricing themselves — the SDK handles all calculations — but understanding the relationships helps when evaluating positions.

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The Core Invariant

The value of one PT plus one YT always equals the value of one SY: PPT+PYT=PSYP_{PT} + P_{YT} = P_{SY} This is the foundation of the entire system. If market prices diverge from this relationship, arbitrage restores the balance.

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PT Price & Implied APY

PT trades at a discount to face value. The size of that discount is your fixed return — and the market expresses it as an implied APY using continuous compounding: PPT=e−APY×tP_{PT} = e^{-\text{APY} \times t} Where tt is time to maturity as a fraction of a year. Higher implied APY means a bigger discount on PT — and a higher fixed return for the buyer. This works in both directions — given a PT price from the market, you can derive the implied APY: APY=−ln⁡(PPT)/t\text{APY} = -\ln(P_{PT}) / t. A quick way to estimate your annualized return without the exponential math: 1−PPTPPT×365d\frac{1 - P_{PT}}{P_{PT}} \times \frac{365}{d}. For moderate rates and short durations both methods give nearly the same number — they only diverge meaningfully at high APYs or long maturities. When PT is priced against SY rather than the base asset, divide by the exchange rate: PPTSY=PPT/rP_{PT}^{SY} = P_{PT} / r. Because SY appreciates over time, PT always appears cheaper in SY terms.

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YT Pricing & Leverage

YT price is the complement of PT, adjusted by the exchange rate: PYT=1−PPTrP_{YT} = \frac{1 - P_{PT}}{r} Because YT costs a fraction of the full asset, it creates inherent leverage on yield. The leverage multiplier is simply 1/PYT1 / P_{YT}: As maturity approaches, PT converges to 1.00 and YT converges to 0 — this is time decay. YT loses value over time even if the underlying rate hasn’t changed, because less time remains to earn yield.

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How Yield Accrues

YT holders earn yield based on the growth of the exchange rate since their position was created. The larger the rate increase, the more SY becomes claimable. Yield accrues continuously and can be collected at any time — you don’t have to wait for maturity. The earned SY for a YT position is calculated from the change in the inverse of the SY exchange rate: earned_SY=YT_balance×(1rlast−1rcurrent)\text{earned\_SY} = \text{YT\_balance} \times \left(\frac{1}{r_{\text{last}}} - \frac{1}{r_{\text{current}}}\right) For example, if a user holds 2,000 YT and the exchange rate moves from 2.0 to 6.0:
After a vault matures, the exchange rate is frozen. Any further appreciation in the underlying protocol does not affect YT yield.

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Fee Decay Model

Both the CLMM and Orderbook use a time-weighted fee model. Fees are highest far from maturity and decay toward zero as the vault approaches expiration: fee_rate=eln_fee_rate_root×τ\text{fee\_rate} = e^{\text{ln\_fee\_rate\_root} \times \tau} Where τ\tau is the normalized time remaining (0 at maturity, 1 at one year out). This reflects the decreasing price uncertainty of PT as it nears redemption — closer to maturity means less risk, so lower fees. The protocol also takes a treasury cut from each trade.