Linear Discount

The linear discount model is commonly used due to its simplicity and its ability to capture the essential behavior of PTs: a steady appreciation toward face value as maturity approaches. It models this convergence through a linear function, and can be viewed as a first-order approximation of traditional bond pricing, substituting exponential growth with a linear interpolation over the term.

The price at time $t$ is given by:

$P(t)=F- \text{baseDiscount} \cdot t$

where $t$ represents time to maturity and $F$ stands for the face value.

Setting the base discount:

There are two principal approaches to determining the base discount:

1. Direct APY assignment: The base discount is often set equal to the current APY at the time of market creation. This method is widely used for its simplicity, but tends to underprice by not accounting for compound interest effects.

2. Calibration to a target initial price: The base discount can be chosen to achieve a desired initial PT price. This approach treats the initial price as the primary input from which the base discount is derived. For example, in a one-year market, setting the base discount to $\frac{F\cdot APY}{1+APY}$ yields an initial price that aligns with the target APY.