Market Interpretation

Inspired by Uniswap, Timeswap uses a unique 3 variable constant product equation:
                                                       X×Y×Z=KX\times Y\times Z=KX×Y×Z=K
 
Where XXX
 = Principal Pool, Y = Interest rate Pool, ZZZ
 = Collateral factor Pool
The market interpretation for variables X,Y,ZX , Y, ZX,Y,Z
 is as follows:
​XXX
 = Principal Pool, where lenders & liquidity providers deposit their assets 
​YYY
 = Interest Rate Pool such that ratio YX\frac{Y}{X}XY​
is equal to the maximum interest rate per second of a pool for a particular token pair at the time of the transaction for the remaining duration of the pool
​ZZZ
 = Collateral factor Pool such that ratio ZX\frac{Z}{X}XZ​
 is equal to the minimum CDP of a pool for a particular token pair at the time of the transaction for the remaining duration of the pool
Let's deep dive into how to use market interpretation with an example:
Alice wants to initialize a DAI-ETH pool with a maturity time of 6 months. She wants to lock 10,000 DAI and expects an annual return of 15% and a CDP of 167% for the given pair and duration.
​X=10000X=10000X=10000
 DAI
​YX=0.1531556926\frac{Y}{X}=\frac{0.15}{31556926}XY​=315569260.15​
(annual interest rate expectation of 15% & number of seconds in a year = 31556926s)
This means Y=0.1531556926×10000=0.0000475Y=\frac{0.15}{31556926}\times10000=0.0000475Y=315569260.15​×10000=0.0000475
 
​ZX=1.67\frac{Z}{X}=1.67XZ​=1.67
 (CDP of 167%), such that the value ofZZZ
is ETH equivalent in DAI
Assuming the price of ETH at the time of pool creation by Alice was 4000DAI, this means the value of Z=10000∗1.674000Z=\frac{10000*1.67}{4000}Z=400010000∗1.67​
 = 4.175 ETH
So Alice can do pool initialization for the DAI-ETH pool with a duration of 6 months, such that variables X=10,000,Y=0.0000475,Z=4.175,K=1.98X=10,000,Y=0.0000475,Z=4.175,K=1.98X=10,000,Y=0.0000475,Z=4.175,K=1.98
​

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