# Continous Auction Specification

### Parameters

A couple of parameters are at play here to make this model work.

Parameter | Unit | ||
---|---|---|---|

Volume Coefficient | Īµ | $t\:CO_2 e$ | Controls how many units of Forward Clip need to be deposited in a single transaction to raise the annualized Time Appreciation rate on offer by 1% for the next deposit |

Discount Floor | Ī± | $t\:CO_2 e$ | Controls how far below the Basket's average Annualized Time Appreciation Rate currently offered D can go. Ie if Ī±=0.5%, the on-offer TA can only go below 0.5% of the Basket's average. |

Decay | Ī» | % / s | Determines how fast the on-offer rate will decrease by decaying the deposit momentum |

Last deposit timestamp | $t_{n-1}$ | s | A timestamp that tracks when the last deposit event occurred. |

Last deposit momentum | $C$ | $t\:CO_2 e$ | A background parameter that is used to roughly track the recent throughput of deposit events. Initialized as $C = Ī±*Īµ*100$, so the first offered rate would start at the Basket average. |

Average time appreciation rate | $D_a$ | % | At key moments calculated as the weighted average of the time appreciation rates of all deposited Forward Clips within the Basket. |

### Deposit math

For any moment in time ($t_n$) and amount (m), the on-offer time appreciation rate (%) is expressed as

Note: The equation uses m/2 instead of m. The logic here is that the depositor claims all available rates between depositing 0 and m. While this can be expressed as a function of $\sum_0^m$, it can be simplified to m/2 due to the linear nature of the rate increase.

Where decayed deposit momentum $V(t_n)$ is defined as

### After deposit updates

**Updating local Forward Clip data**

If some supply from that specific Forward Clip has been deposited before, we need to update the local time appreciation for that Forward Clip. To do this, we need to know the FC's current local time appreciation rate $D_l$, local deposited supply M_l and local time to delivery $N_l$.

Defining outstanding ERC-20 supply related to a given Forward Clip as

We can update local time appreciation as

Finally, we update$M_l$

**Updating Basket's deposit momentum**

C is updated as

**Updating Basket's last deposit timestamp**

Then R is recalculated and $t_{n-1}$ *is set to the value of *$t_n$

**Updating Basket's average time appreciation**

Simple weighted average using new deposited amount and related time appreciation parameter and previous Basket deposit total and average time appreciation

Last updated