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:

    Gd=IntersectΒ Incomed+π‘‡π‘Ÿπ‘Žπ‘›π‘ π‘Žπ‘π‘‘π‘–π‘œπ‘›Β πΉπ‘’π‘’π‘ π‘‘βˆ’πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘Β πΈπ‘₯𝑝𝑒𝑛𝑠𝑒𝑑G_d = {Intersect\ Income_d} + {π‘‡π‘Ÿπ‘Žπ‘›π‘ π‘Žπ‘π‘‘π‘–π‘œπ‘›\ 𝐹𝑒𝑒𝑠_𝑑} βˆ’ {πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘\ 𝐸π‘₯𝑝𝑒𝑛𝑠𝑒𝑑}

    • π‘€β„Žπ‘’π‘Ÿπ‘’ π‘‘β„Žπ‘’π‘ π‘’ π‘–π‘›π‘π‘œπ‘šπ‘’/𝑒π‘₯𝑝𝑒𝑛𝑠𝑒 π‘–π‘‘π‘’π‘šπ‘  π‘Žπ‘Ÿπ‘’ π‘Žπ‘‘π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘Žπ‘π‘™π‘’ π‘‘π‘œ 𝑙𝑒𝑛𝑑𝑠/π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘  π‘€π‘–π‘‘β„Ž π‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› β‰₯ 𝑑.

  2. 𝐼𝐹(πΈπ‘žπ‘’π‘–π‘‘π‘¦π‘‘β‰€πΊπ‘‘Β β†’Β π‘π‘Žπ‘’π‘ π‘’Β π‘“π‘’π‘Ÿπ‘‘hπ‘’π‘ŸΒ π‘™π‘’π‘›π‘‘π‘–π‘›π‘”πΌπΉ(πΈπ‘žπ‘’π‘–π‘‘π‘¦_𝑑 \le 𝐺_𝑑\ β†’\ π‘π‘Žπ‘’π‘ π‘’\ π‘“π‘’π‘Ÿπ‘‘β„Žπ‘’π‘Ÿ\ 𝑙𝑒𝑛𝑑𝑖𝑛𝑔 for durations ≀d\le d

    • πΈπ‘žπ‘’π‘–π‘‘π‘¦π‘‘ π‘Ÿπ‘’π‘π‘Ÿπ‘’π‘ π‘’π‘›π‘‘π‘  π‘‘π‘œπ‘‘π‘Žπ‘™ π‘π‘œπ‘œπ‘™ π‘’π‘žπ‘’π‘–π‘‘π‘¦ π‘“π‘œπ‘Ÿ π‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘  β‰₯ 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 βˆ’ ii. LP funds exited from pool + iii. Pool transaction fee searned + iv. Pool interest earned βˆ’ v. Pool interest paid βˆ’ vi. Other losses / expenses]

  2. Pool Entry

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

    b. Discount = (YminYmax)Γ—(DDmax)(\frac {Y_{min}} {Y_{max}}) \times (\frac {D} {D_{max}})

    i. where D is LP duration

    ii. DminD_{min} and DmaxD_{max} are the minimum and maximum durations of the yield curve

    iii. YminY_{min} and YmaxY_{max} are corresponding yields

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

  3. Pool Exit

    a. LPexit=%Β ownedΒ byΒ LPexitΓ—PoolΒ NAVLP_{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 Γ—\times (1 + Percentage of pool owned by exiting LP)

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