System Parameters

A operational description of Checker’s internal parameters, and operations on them. NOTE: here we focus primarily on the specifics of the calculations; for the meaning of the concepts, see Design.


  • q: of type (1 / kit).

  • index: of type tez.

  • protected_index: of type tez.

  • target: TODO: said dimensionless, but I think tez/kit? Hmmm. I have to re-check the units of measure.

  • drift_derivative

  • drift

  • outstanding_kit: approximation of the total amount of kit that would be currently required to close all burrows.

  • circulating_kit: approximation of the total amount of kit that is currently in circulation.

  • last_touched: the last time the parameters were touched.

And two additional indices, one used in the calculation of burrowing fees and one in the calculation of the imbalance adjustment:

  • burrow_fee_index

  • imbalance_index


We currently initialize checker with the following parameters:

q = 1
index = 1xtz
protected_index = 1xtz
target = 1
drift = 0
drift_derivative = 0
outstanding_kit = 0mukit
circulating_kit = 0mukit
last_touched = now
burrow_fee_index = 1
imbalance_index  = 1

Price API

tz_minting     = max index protected_index (in tez)
tz_liquidation = min index protected_index (in tez)

To calculate the current prices in (tez/kit), we multiply with the current quantity:

minting_price     = q * tz_minting
liquidation_price = q * tz_liquidation


The definition of tz_minting and tz_liquidation implies that at any given moment, tz_minting >= tz_liquidation > 0. Combined with fminting > fliquidation, we have that

tz_minting * fminting > tz_liquidation * fliquidation

which is useful in liquidation logic (see

Adjustment index

The adjustment index, as required by burrowing logic, can be calculated from the system parameters as the product of the burrow fee index and the imbalance index:

adjustment_index = burrow_fee_index * imbalance_index


Touching the system parameters has the effect of updating all aforementioned fields, and calculating the burrowing fees that need to be accrued to the cfmm sub-contract. This is done under the assumption that we have available the current time now, the current index index_now (calculated by the medianizer), and the current price of kit in tez kit_in_tez_now (calculated by the cfmm sub-contract). In fact, the cfmm sub-contract gives us the one calculated at the end of the last block, to make manipulation a little harder. We update each field:


Update the timestamp from the last time it was touched to now

new_last_touched = now


Update the index from the last time the parameters were touched to the current one

new_index = index_now


Update the protected index, by multiplying it with a bounded factor:

new_protected_index = old_protected_index * clamp (current_index / protected_index, low, high)

where low and high depend on how much time has passed since the last time the parameters were touched, effectively limiting how fast protected_index can change:

low  = exp (-epsilon * (now - last_touched))
high = exp (+epsilon * (now - last_touched))

NOTE: exp (x) = 1 + x here; we expect the contract to be touched rather frequently, which keeps the exponent rather small, which makes this a good approximation of exp.


For the calculation of the derivative of drift, drift_derivative, we only use the last-observed target (TODO: show how we get from the original formula with the logarithms to this?) We calculate as follows:

new_drift_derivative =
  -0.0005 / (secs_in_a_day ^ 2) , if                        target <= exp (-high_bracket)
  -0.0001 / (secs_in_a_day ^ 2) , if exp (-high_bracket) <  target <= exp (-low_bracket)
   0                            , if exp (-low_bracket)  <  target <  exp ( low_bracket)
   0.0001 / (secs_in_a_day ^ 2) , if exp ( low_bracket)  <= target <  exp ( high_bracket)
   0.0005 / (secs_in_a_day ^ 2) , if exp ( high_bracket) <= target


For the calculation of the current drift, we use use the following formula:

new_drift = old_drift + (1/2) * (old_drift_derivative + new_drift_derivative) * (now - last_touched)


For the calculation of the current quantity q, we use the following formula:

new_q = old_q
      * exp (
          (old_drift + (1/6) * ((2 * old_drift_derivative) + new_drift_derivative) * (now - last_touched))
          * (now - last_touched)

NOTE: exp (x) = 1 + x here; TODO: not sure if the exponent is small enough for this to be a good approximation.


new_target = new_q * (new_index / kit_in_tez_now)


The burrow fee index is updated linearly on the number of seconds that have passed since the last time the parameters were touched.

new_burrow_fee_index = old_burrow_fee_index
                     * (1 + burrow_fee_rate * (now - last_touched) / seconds_in_a_year)


The imbalance index is also updated linearly on the number of seconds that have passed since the last time the parameters were touched

new_imbalance_index = old_imbalance_index
                    * (1 + imbalance_rate * (now - last_touched) / seconds_in_a_year)

but imbalance_rate varies, depending on the difference between old_outstanding_kit and old_circulating_kit:

imbalance_rate =
    ( imbalance_scaling_factor * (circulating - outstanding) / circulating,

or, equivalently:

imbalance_rate =
  min (imbalance_scaling_factor * (circulating - outstanding) / circulating, +imbalance_limit), if circulating >= outstanding
  max (imbalance_scaling_factor * (circulating - outstanding) / circulating, -imbalance_limit), if circulating < outstanding

And in the edge cases the imbalance_rate is calculated as follows:

  • if old_circulating_kit = 0 and old_outstanding_kit = 0 then imbalance_rate = 0.

  • if old_circulating_kit = 0 and old_outstanding_kit > 0 then imbalance_rate = -imbalance_limit. (the outstanding kit is infinitely greater than the circulating kit, so the rate is saturated).

Intermediate outstanding_kit

In order to compute the updates for the two remaining fields (outstanding_kit and circulating_kit), we first need to calculate the current amount of kit outstanding, taking into account the accrued burrowing fee, thus

outstanding_with_fees = old_outstanding_kit * (new_burrow_fee_index / old_burrow_fee_index)

Accrual to cfmm

The accrued burrowing fees are to be given to the cfmm sub-contract. The total amount we easily compute as

accrual_to_cfmm = outstanding_with_fees - old_outstanding


To obtain the updated outstanding_kit, we need to account for both the accrued burrowing fees, and the imbalance adjustment

new_outstanding_kit = old_outstanding_kit
                    * (new_burrow_fee_index / old_burrow_fee_index)
                    * (new_imbalance_index / old_imbalance_index)

or equivalently

new_outstanding_kit = outstanding_with_fees * (new_imbalance_index / old_imbalance_index)


Finally, to obtain the up-to-date circulating_kit, we just need to record the new kit in circulation, that is, accrual_to_cfmm:

new_circulating_kit = old_circulating_kit + accrual_to_cfmm

NOTE: If the current timestamp is identical to that stored in the parameters, we do not perform any of the above.


  • seconds_in_a_year = 31556952 (= (365 + 1/4 - 1/100 + 1/400) days * 24 * 60 * 60)

  • seconds_in_a_day  = 86400 (= 24 * 60 * 60)

  • low_bracket  = 0.005

  • high_bracket = 0.05

  • imbalance_scaling_factor = 0.75

  • imbalance_limit = 0.05