Examples
Approach
We have 4 pools:
A liquidity pool (L pool) with a pool of DAI and a pool of ETH.
The L pool is the pool used by the exchange to borrow assets for the hedging.
An exchange pool (E pool) with a pool of DAI and a pool of ETH The E pool is the pool kept by the exchange to remain solvent at any time and this is where the hedges are stored.
Assumptions
The spot price of ETHDAI is equal to 100
There is no leverage, i.e. all positions are fully funded
There are no transaction fees
We consider a yearly futures
The borrowing rate is determined using the Aave formulas which depend on the utilisation ratio of each pool
The futures prices are derived using the borrowing rates of each asset.
Buy example
Pricing
The initial pool is as below:
Tot Borrow
Tot Liquidity
Utilisation rate
U_optimal
Base
Slope 1
Slope 2
Borrowing rate
DAI
2500
10000
25.00%
80%
0%
4%
75%
1.25%
ETH
10
1000
10.00%
65%
0%
8%
100%
1.23%
A user wants to buy 1 futures, hence the new liquidity pool would be
Tot Borrow
Tot Liquidity
Utilisation rate
U_optimal
Base
Slope 1
Slope 2
Borrowing rate
DAI
2600
10000
26.00%
80%
0%
4%
75%
1.30%
ETH
10
1000
10.00%
65%
0%
8%
100%
1.23%
The price to buy 1 futures is P=100*exp(1*0.013)=101.31
Execution
Trader buys 1 ETH at 101.31 DAI on the futures market
Protocol borrows 100 DAI at 1.3% from the B pool and hence will owe 100*exp(0.013)=101.31 DAI in 1 year
Protocol buys 1 ETH with the borrowed DAI and put them in the E pool.
Sell example
Pricing
The initial pool is as below:
Tot Borrow
Tot Liquidity
Utilisation rate
U_optimal
Base
Slope 1
Slope 2
Borrowing rate
DAI
2500
10000
25.00%
80%
0%
4%
75%
1.25%
ETH
10
1000
10.00%
65%
0%
8%
100%
1.23%
A user wants to sell 1 futures, hence the new liquidity pool would be
Tot Borrow
Tot Liquidity
Utilisation rate
U_optimal
Base
Slope 1
Slope 2
Borrowing rate
DAI
2500
10000
25.00%
80%
0%
4%
75%
1.25%
ETH
11
1000
11.00%
65%
0%
8%
100%
1.35%
The price to sell 1 futures is P=100*exp(-1*0.0135)=98.66
Execution
Trader sells 1 Futures for 98.66 DAI on the futures market
Protocol borrows 0.9866 ETH from the liquidity pool at 1.35% and hence will owe 0.9866*exp(1*0.0135)=1ETH in 3 months
Protocol sells 0.9866 ETH in the spot market for 98.66 DAI
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