Setting Interest Rates for ETH Instant Unstake Loans

We will need to establish an accurate and fair pricing model for our Instant Unstake Model. Our algorithms must solve for a range of parameters, but arguably the most critical is the borrow interest rate/discount rate at which we will price the Instant Unstake purchases.

How do We Build the Discount Rate in Our Model?

Within the context of a P2Pool system our interest rate will be determined by available liquidity in the system. Of course that liquidity can take several shapes:
  1. 1.
    ETH and WETH
  2. 2.
    aETH, cETH, stETH, and/or other ETH derivatives on ParaSpace
Within the P2P/P2Pool hybrid model we will likewise add a marketplace for these stakefish staking NFT’s and outright P2P purchases. Below is the schematic of the ParaSpace Instant Unstake NFT router:
Staking derivative NFT router on ParaSpace
Here we focus on step 1. as this itself will be its own router within the above tokens.
Within Step 1:
  • Calculate the instantaneous borrow rate
    BorrowAPYETHBorrowAPY_{ETH}
    from the ParaSpace Pool.
  • Calculate the instantaneous borrow rate
    BorrowAPYaETHBorrowAPY_{aETH}
    ,
    BorrowAPYcETHBorrowAPY_{cETH}
    , and Borrow APY’s for stETH/wstETH, cbETH, and rETH. Implicit in this is the assumption that we would be able to redeem/trade via 1inch the ETH derivative at par value via each respective protocol.
  • Pick the lowest instantaneous
    BorrowAPYBorrow_{APY}
    for ETH among the various ETH and ETH derivative pools.
  • NB: Implicit in the above is that instantaneous loans have zero duration risk. But as we will discuss in the next section we will need to adjust borrow rates for the relevant duration risk.
Of course even beyond the stakefish NFT router we want to know how much a specific staking position is worth. And indeed we study pricing models and setting interest rates for these loans below.

Duration Risk and Overcollateralized DeFi Loans

The well-understood Aave/Compound lending model creates overcollateralized open-ended loans with no specific requirement nor immediate need to assign duration risk to the loan. Or in other words, the borrower pays the same interest rate regardless of how long they maintain their borrow position. Why?
  • Overcollateralization with quality collateral means the lender can recoup any principal and interest owed upon a successful liquidation.
  • As long as there is sufficient liquidity available and low utilization, Lenders may at any point withdraw principal + interest with no credit risk. Their discount rate could be infinite but Present Value of cash flow
    Principal+Interest(1+rDiscount365)T\frac{Principal + Interest }{(1+\frac{r_{Discount}}{365})^T}
    is always divided by 1 if days
    TT
    until payment of
    Principal+InterestPrincipal + Interest
    is 0.
There nonetheless remains duration risk for both the borrow and the lender, specifically with regard to interest rates:
  • Lender: Given that interest rates vary by Utilization, the Lender may receive a worse return than they anticipated if Utilization within the pool declines. Both of these risks grow as a function of Duration and Utilization:
    • The interest rate may in fact drop below the Lender’s discount rate and thus this may prove unprofitable. This can also be referred to as Convexity risk, or the change in value of an existing lending position on a rise or fall in its interest rate.
    • Utilization may hit 100% and the Lender will be unable to withdraw their Principal + Interest, extending days
      TT
      until redemption when liquidity returns.
  • Borrower: The Borrower may ultimately pay a higher interest rate than they expected if Utilization rises.
    • This interest rate may rise above the Borrower’s discount rate and this borrow may prove unprofitable. This risk grows as a function of Duration and Utilization.

Summarizing Risks Inherent to ETH Unstaking Loans - Duration/Convexity and Slashing

In order to make capital-efficient and risk-controlled loans against ETH Staking, our protocol and liquidity suppliers will need to account for risks specific to Duration and Staking. Our Borrow Interest rate, or
rBorrowr_{Borrow}
, will thus need to account for three risks which are all a function of or impacted by time to redemption in days
TT
:
  1. 1.
    Interest rate risk - the likelihood that interest rates will vary significantly from the time of Instant Unstake to redemption through days
    TT
    . We can likewise refer to this as Convexity Risk—the likelihood that the value of the outstanding loan will change with a change in interest rates.
  2. 2.
    Liquidity risk - This is the risk that ETH pool Utilization will surge and leave the ETH supplier without the ability to withdraw their Principal and Interest. Notably Interest Rates are a function of Utilization thus this is closely linked to Interest rate risk.
  3. 3.
    Slashing risk - In practice the slashing risk is very low but non-zero. We can safely ignore Slashing risk for shorter-term loans, though it is ultimately a function of validator quality and time
    TT
    .
All three are a function of time
TT
and will be grouped under the broader umbrella of Duration Risk.
In each of these, risk will be greater for lending against lower-liquidity collateral. In practice we will focus on top staking derivative protocols and will not price in Slashing Risk to our valuation algorithms.

Addressing Interest Rate Risk and Liquidity Risk - the Duration Factor

We reference Interest Rate Risk and Liquidity Risk as two distinct risks and they are, but in practice Interest Rates are a function of Utilization and thus liquidity. Or in short: our pricing of Interest Rate (Convexity) and Liquidity Risk will be one in the same. We will indeed refer to this as Duration Factor, or
DFDF
for short.
  1. 1.
    At time of pricing specific staking derivative Instant Unstake rates we will gather the best borrow rate
    r0r_0
    from our ETH liquidity sources. This will serve as the minimum Discount rate.
  2. 2.
    We determine that it will take
    TT
    days for the staking derivative token to be redeemed at the redemption rate in ETH based on our evaluation protocols.
  3. 3.
    We will thus calculate a Duration Factor
    DFDF
    for duration/convexity risk.
    DFDF
    will be defined as a number
    >1>1
    such that each increment of
    TT
    will add
    1DF\frac{1}{DF}
    interest rate risk to the Instant Unstake request.
  4. 4.
    Calculate
    rDiscountr_{Discount}
    with the following equation:
rDiscount=rVendor+r0×TDFr_{Discount} = r_{Vendor} + \frac{r_0 \times T }{DF}
The above equation can give us
rTr_T
at the origination of the loan, or time
t=0t=0
. If at a future point we would like to calculate the updated
rTr_T
we would rewrite the equation as the following, more generalized, equation:
rDiscount+t=rVendor+rt×(Tt)DFr_{Discount+t} = r_{Vendor} + \frac{r_t \times (T-t) }{DF}
We represent the passage of time
tt
as the days elapsed since the loan was first made and we would re-calculate based on the contemporaneous
rtr_t
to represent the best ETH borrow rate available at the time. Necessarily this likewise means the value of the Instant Unstake loan will vary based on ETH pool utilization and time. And indeed there will implicitly be Duration and Convexity risk on the outstanding loan.

Pricing the Aggregate Borrow and Discount Rate for Instant Token Unstake

With the above information to hand, we can now calculate the aggregate
rTr_{T}
and ultimately the
rDiscountr_{Discount}
rate we will use to price the Instant Unstake for the staking derivative tokens.
rDiscount=rTr_{Discount} = r_T
We can then price our instant unstake position of either LSD tokens or a staking position as follows. Since we are working with only the highest quality Staking as a Service providers we will assume
RedemptionETHRedemption_{ETH}
= 1 given a staking risk of 0. We can thus express our Instant Unstake value as follows:
PrincipalTotal×RedemptionETH(1+rDiscount365)T\frac{Principal_{Total} \times Redemption_{ETH}}{(1+\frac{r_{Discount}}{365})^T}
Our on-chain oracle will thus calculate the following figures to a high degree of accuracy to ensure liquidity providers are appropriately compensated for Instant Unstake purchases:
  • TT
    days until redemption
  • RedemptionETHRedemption_{ETH}
    if different to 1:1.
Below is a chart of the Present Value/Instant Unstake amount of 1 ETH due to be redeemed in days
TT
at a base
r0r_0
of 10%. Notably a
DFDF
of 365 implies
rDiscountr_{Discount}
would double
r0r_0
at
T=365T=365
days using the equation
rDiscount0=r0+r0×TDFr_{Discount_0} = r_{0} + \frac{r_0 \times T }{DF}
.

Instant Unstake Swap Rate Projections

Data and chart source: ParaSpace calculations
By way of example, a user may request an Instant Unstake of a 32 ETH staking NFT with a redemption rate of 1.000 due to be redeemed in 10 days. According to the above equations the ParaSpace pool would be able to pay them 31.9125 ETH at an
rDiscountr_{Discount}
of 10%.

Establishing DF Value For ETH Staking Derivatives

Given that we are focused on only top-quality Ethereum staking derivatives, we will focus not on the quality of the collateral used but instead liquidity conditions in the ETH money market on ParaSpace. We expressly build in the current pool Utilization rate
UU
into
rDiscount0=r0+r0×TDFr_{Discount_0} = r_{0} + \frac{r_0 \times T }{DF}
as
r0r_0
, or the interest rate at
t=0t=0
, is purely a function of pool liquidity as measured by Utilization.
Our setting for
DFDF
will aim to make borrowing more expensive if the liquidity will be tied to that specific position for extended times
TT
. What is a reasonable rate at which
rDiscountr_{Discount}
will double?
It is difficult to estimate the total term of loans in the P2Pool lending model and as such we need to look beyond pure DeFi to estimate average loan duration. According to on-chain data for P2P NFT lending, lenders and borrowers on average agree to a 30-day average lending term for P2P NFT loans. But in this case the quality and liquidity of collateral is ETH staking positions—the more conservative number makes sense here.
We will set
DFDF
to a value at which
rDiscountr_{Discount}
will be
r0×2r_0 \times 2
at a loan term of 90 days, or
DF=90DF = 90
, as our risk-based collateral factor for ETH itself is 3x that of lower-tier Art and Collectible NFT Collections.
Below we see how
rDiscountr_{Discount}
and the instant-purchase value of 1 ETH varies by time
TT
until Redemption with an
r0r_0
of 10% and
DFDF
of 90.
Duration factor of 90 chart
Our model is quite intentionally straightforward but ultimately protocol usage for these fixed-term redemptions will be a function of supply and demand. A
DFDF
of 90 thus acts as a starting point and may be adjusted based on community feedback and eventually DAO-governed votes.

Setting Protocol Insurance Reserve and Supplier Rates

ParaSpace looks to generate value to the end user and in the process generate funds for future protocol growth. In doing so we will add an insurance reserve to the
rDiscountr_{Discount}
rate, currently set at 10% across all ERC20’s.
We can thus calculate the share of each Instant Unstake of NFT discount which goes to the supplier and which share goes to the protocol insurance reserve.
At t0:PrincipalUnstake=PrincipalTotal(1+rDiscount365)TAt \ t_0: Principal_{Unstake} = \frac{{Principal_{Total}} }{(1+\frac{r_{Discount}}{365})^T}
At time of redemption
TT
, the supplier pool receives:
At tT:PrincipalSupplier=PrincipalUnstake×(1+rDiscount×(1fReserve)365)TAt \ t_T: Principal_{Supplier} = Principal_{Unstake} \times {(1+\frac{r_{Discount} \times (1-f_{Reserve})}{365})^T}
We can thus calculate the share of each token sale which goes not to the supplier pool but to the insurance protocol reserve as indicated below. The area under 1.000 indicates the share which goes to the Protocol Reserve:
Protocol Reserve fees and Instant Unstake swaps