Pricing Mechanism

The price formula is:

$$\text{price}(t) = \frac{1}{\text{rateScalar}(t)} \times \ln\left(\frac{p(t)}{1 - p(t)}\right) + \text{rateAnchor}(t)$$

• Normalized time ( t ) ranges from 0 (maturity) to 1.

• rateScalar: $\text{rateScalar}(t) = \frac{\text{ScalarRoot}}{t}$

• rateAnchor adjusts dynamically to maintain capital efficiency.

Example:

Given$( \text{rateScalar} =100)$, $( \text{rateAnchor} = 1.1 )$， initial PT proportion $( p_{\text{before}} = 0.6 )$

$$\text{price}_{\text{before}} = \frac{1}{100} \times \ln\left(\frac{0.6}{0.4}\right) + 1.1 = 1.104055$$

After swapping 100 BT for PT, assuming $p_{\text{after}} = 0.55$

$$\text{price}_{\text{after}} = \frac{1}{100} \times \ln\left(\frac{0.55}{0.45}\right) + 1.1 = 1.102007$$

$$dPT = 100 \times \frac{1.104055 + 1.102007}{2} = 110.202785$$