Mint

Minting is how a user enters the BSM protocol. A user deposits a quantity of the PGOLD into the custodian contract and specifies one thing: the amount of PGUSD he wants to withdraw. The protocol then splits the deposited collateral into two tokens issued simultaneously — the PGUSD and the LPGOLD — in proportions determined by the chosen tier. The combined dollar value of the two tokens always equals the value of the collateral deposited, so nothing is created out of thin air.

The PGUSD token the user receives is worth exactly 1 unit of account and never changes. The LPGOLD token's value, on the other hand, moves with the price of the underlying asset . The higher the leverage tier, the more amplified that movement is in both directions. Once minted, the user holds both tokens freely and can trade them independently on secondary markets or through the AMM.

When a user mints, they stake an amount of PGOLD (denoted as $N_S$ into the protocol. The user can then withdraw up to PGUSD not exceeding the maximum loan-to-value ratio ( $LTV_{MAX}$).

Suppose at the initial time the user withdraws an amount $N_S$ of PGUSD, leaving a remaining balance of $N_L$ in LPGOLD. Given that the price of PGOLD is , the following relationship must hold:

$$N_S*1+N_L*1 = N_G * P_0$$

$$LTV_0 = \frac{N_S}{N_G*P_0}$$

At time t, the price of PGOLD changes from P_0 to P_t. At this moment, the net asset value of the L token is denoted as $NAV_t$,

$$N_S*1+N_L*NAV_t = N_G * P_t$$

$$LTV_t = \frac{N_S}{N_G*P_t}$$

$$NAV_t = \frac{N_G*P_t - N_S}{N_L} = (\frac{1}{LTV_t}-1)*\frac{N_S}{N_L}$$