Choosing Linear Discount Parameters

In this documentation, we provide a Desmos graphic that let you fill in parameters to help visualizing and choosing a good linear discount rate for the linear discount oracle.

Desmos link: https://www.desmos.com/calculator/xmtoxy6lkt

The Desmos link contains the example for the USDe 25 SEP 2025 market.

• PT linear discount rate can be chosen to be $18\%$.
• LP linear discount rate can be chosen to be $7\%$.

See this in the Desmos graphic by changing $r_{discount}$ in the corresponding folder.

Parameters

Market internal state

The Desmos graphic requires some internal state of the Pendle market. The following notebook can be used to get the market’s internal state: https://colab.research.google.com/drive/1CKltGGLWrdUoCVRpV1U9ZV2BqjMkN_OE?usp=sharing

For example, if the chosen market is USDe 25 SEP 2025 market, the parameters can be obtained like the image on the left, and be filled as the image on the right.

Running the notebook	Filling the parameters in Desmos

Market yield range

These parameters are opinionated. Please choose a yield range that you think the market will be trading in until maturity. The lower the $\text{rateMax}$, the less underprice the oracle will be, and the more capital efficient for the users.

Pendle Market also allows trading within a pre-determined yield range. If you are not sure about the yield range, use this.

This yield range can be obtained from the Pendle DApp UI:

Click the spec button	Getting the yield range

And filled it as the following:

Choosing between PT linear oracle and LP linear oracle

The Desmos graphic can help visualize both linear discount. The corresponding graphic can be toggled by clicking the corresponding folder

Choosing the linear discount rate

In both graphic:

• The blue lines are the maximum and minimum price of PT/LP (the price range).
• The orange line is the current price of PT/LP until maturity if there is no trade occurred.
• The red line is the discounted price of PT/LP with your discount rate.

Change $r_{discount}$ to adjust the discounted price (the red line) and see its relation between the price range and the current price.

Base price (or the matured price)

For PT, since it can be redeem to asset 1:1 at maturity, the base price of PT is 1.

For LP, the base price is calculated in the Desmos graphic. It can be found in the LP linear discount Desmos folder:

Recommendation

$r_{discount}$ should be set so that the price is sub-optimal compare to the market price at all the time until maturity. Therefore:

• The discounted price line should be below the current price.
• The closer the discounted price line to the current price, the riskier.
• Setting $r_{discount}$ so that the discounted price line is under the lower price line can make sure that the oracle price is always underpriced.

Reference

• https://forum.sky.money/t/june-26-2025-proposed-changes-to-spark-for-upcoming-spell/26663 — Spark write up on linear discount rate for PT-syrupUSDC-28Aug2025, PT-USDe-25Sept2025, LP-USDS-14Aug2025.
• https://www.desmos.com/calculator/n7wfzslz8l — Desmos graphic for single trade on Pendle Market.