Linear Discount Model

The linear discount model is a pricing model for the Principal Token (PT) that assumes the PT discount evolves linearly in time. At start time, the model prices the PT as its par value discounted by the non-compounded instantaneous rate $r$ over the term. At maturity, the model prices the PT at its par value. The model linearly interpolates between those two points. More specifically

$$P(t,T) = \alpha(t) (1 - \frac{1}{1 + r(T-t)})\frac{t}{T} + \frac{\alpha(t)}{1 + r(T-t)}$$

In this equation, $\alpha(t)$ represents the ptRate at time $t$, i.e the par value of the PT, $T$ is the maturity timestamp, while $t$ is the current timestamp.