Liquidity Swaps

What are Liquidity Swaps?

The AMO can perform liquidity swaps with the Stability Pool. A DUCA Swap will send in DUCA that is valued at the Exchange Value and return DCM valued at its Market Value. A DCM Swap sends in DCM valued at its Exchange Value which returns DUCA valued at its Exchange Value. These swaps form the basis of the stability mechanism of DUCA within the Protocol.

DCM EXCHANGE VALUE

$\mathrm{DCM\ Market\ Value} > \mathrm{DCM\ Par\ Value} ; \quad \mathrm{DCM\ Exchange\ Value} = \mathrm{DCM\ Market\ Value}$

$\mathrm{DCM\ Market\ Value} < \mathrm{DCM\ Par\ Value} ; \quad \mathrm{DCM\ Exchange\ Value} = \mathrm{DCM\ Par\ Value}$

DCM / DUCA SWAP

$\mathrm{DUCA} = \mathrm{DCM_{In}} \times \mathrm{DCM\ Exchange\ Value}$

DUCA / DCM SWAP

$\mathrm{DCM} = \frac{\mathrm{DUCA_{In}}}{\mathrm{DCM\ Market\ Value}}$

What is Seigniorage?

When DUCA or DCM are trading below their minimum values a Seigniorage (tax) will be applied to the swaps to avoid value extraction from the Protocol that destabilises the Protocol. A negative outcome of the calculation means the Seigniorage is 0. The Seigniorage will be paid in DCM and added to the DUCA Treasury.

DCM / DUCA SWAP

$\mathrm{Seigniorage} = \mathrm{DCM\ Par\ Value} - \mathrm{DCM\ Market\ Value}$

$\mathrm{DUCA} = \mathrm{DCM_{In}} \times (\mathrm{DCM\ Par\ Value} - \mathrm{Seigniorage})$

DUCA / DCM SWAP

$\mathrm{Seigniorage} = 1 - \mathrm{DUCA\ Market\ Value}$

$\mathrm{DCM} = \frac{(\mathrm{DUCA_{In}} - (\mathrm{DUCA_{In}} \times \mathrm{Seigniorage}))}{\mathrm{DCM\ Market\ Value}}$