Where: X= reserves of Collateral Claim Token 1 tokens in the pool Y= reserves of Collateral Claim Token 2 tokens in the pool Z= reserves of Bond tokens(BT) per second in the pool K= Constant Product Invariant
X = Collateral claim pool(Token 1), where Borrowers withdraw CCT for their borrowing positions.
Y= Collateral claim pool(Token 2), where Borrowers withdraw CCT for their borrowing positions
Z= Bond pool, where lenders withdraw BT as a yield for their positions.
I is the marginal interest rate per second = Z / (X+Y) . It determines the interest rate for lenders and borrowers of the pool.
K = Transition / Strike Price. The price at which a borrower decides whether or not he wants to exercise his right to sell the locked collateral to the lenders is what we are calling the transition price, which in the context of the options is simply the strike price. It also determines the CDP of loans on Timeswap.
The Selection of Transition Price is crucial since it determines the APR and CDP of the pool. If the Transition price (K) is closer to Spot Price(S), then the pool will have a High APR and Low CDP, whereas if Transition price (K) is farther away from Spot Price (S), the pool will have Low APR and High CDP. Refer to the image below to understand this better:
Example - Suppose a Liquidity Provider wants to create USDC/ETH pool with 10% APR, 1000 USDC per ETH Strike (K), and 1 Year maturity (d). Assume the Spot price (S) to be 900 USDC per ETH.
Marginal interest rate I is :
I=Z/(X+Y)=10/100=(10/100)/d. It represents Interest rate=10% annually= 10/100 annually= (10/100)/d per second d= 31557600 seconds (represents 1-year maturity)
X= 10. This represents 10 CCT ETH tokens are in the pool.
Y= 0. This represents 0 CCT USDC in the pool. This is because Borrowers cannot borrow 1000 USDC by locking 1 ETH(worth 900 USDC only).
Z= 1/31557600, (dZ=1). It is the amount of BT in the pool, which maintains the ratio in Interest Rate
Read Liquidity Provision section to understand the pool creation calculations and mechanics in detail: