Liquidity Provision

The AMM liquidity pool is bootstrapped with equity from LPs and notional interest units (iX) are created as desired to set up an initial yield curve in line with the reference market.

The LP position is an equity position designed to manage the AMM’s balance sheet. The below formulas ensure an optimal amount of pool equity with capital adequacy and efficiency:

1. Let the income gap be defined as follows:

   $G_d = {Intersect\ Income_d} + {𝑇𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛\ 𝐹𝑒𝑒𝑠_𝑑} − {𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡\ 𝐸𝑥𝑝𝑒𝑛𝑠𝑒𝑑}$

   • 𝑤ℎ𝑒𝑟𝑒 𝑡ℎ𝑒𝑠𝑒 𝑖𝑛𝑐𝑜𝑚𝑒/𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑖𝑡𝑒𝑚𝑠 𝑎𝑟𝑒 𝑎𝑡𝑡𝑟𝑖𝑏𝑢𝑡𝑎𝑏𝑙𝑒 𝑡𝑜 𝑙𝑒𝑛𝑑𝑠/𝑏𝑜𝑟𝑟𝑜𝑤𝑠 𝑤𝑖𝑡ℎ 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ≥ 𝑑.

2. $𝐼𝐹(𝐸𝑞𝑢𝑖𝑡𝑦_𝑑 \le 𝐺_𝑑\ →\ 𝑝𝑎𝑢𝑠𝑒\ 𝑓𝑢𝑟𝑡ℎ𝑒𝑟\ 𝑙𝑒𝑛𝑑𝑖𝑛𝑔$ for durations $\le d$

   • 𝐸𝑞𝑢𝑖𝑡𝑦𝑑 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑜𝑙 𝑒𝑞𝑢𝑖𝑡𝑦 𝑓𝑜𝑟 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑠 ≥ 𝑑

The following points describe the structure of an LP position:

1. NAV(Net Asset Value)

   a. Cumulative since pool inception [i. LP funds provided to pool − ii. LP funds exited from pool + iii. Pool transaction fee searned + iv. Pool interest earned − v. Pool interest paid − vi. Other losses / expenses]

2. Pool Entry

   a. Percentage of pool owned by entering LP = $\frac {LP\ Amount} {[NAV \times (1 - Discount)] + LP\ Amount}$

   b. Discount = $(\frac {Y_{min}} {Y_{max}}) \times (\frac {D} {D_{max}})$

   i. where D is LP duration

   ii. $D_{min}$ and $D_{max}$ are the minimum and maximum durations of the yield curve

   iii. $Y_{min}$ and $Y_{max}$ are corresponding yields

   c. Updation of all other LP stakes whenever an LP enters => Percentage of pool owned by any other LP $\times$ (1 - Percentage of pool owned by entering LP)

3. Pool Exit

   a. $LP_{exit} = \%\ owned\ by\ LP_{exit} \times Pool\ NAV$

   b. Updation of all other LP stakes whenever an LP exits => Percentage of pool owned by any other LP $\times$ (1 + Percentage of pool owned by exiting LP)