Market Driven Mint

At the core of Nirvana is the Market Driven Mint (MDM), the fully autonomous, algorithmic pricing engine that serves as the primary marketplace for ANA. The MDM ensures that every ANA token in circulation is backed by a rising floor price.

The rising floor price of ANA is embedded in the simple mathematics of the MDM’s pricing function, which operates according to a few key principles:

• The MDM’s pricing function is fully deterministic and predictable. Buying ANA drives the price up, while selling ANA causes the price to drop—though never below the floor.

• Every ANA token in existence must be minted through the MDM. Each token was originally purchased from the MDM, with the proceeds held in its reserves.

• When an ANA token is sold back to the MDM, it is burned (removed from circulation), and the corresponding amount of cash from the MDM’s reserves is paid to the seller.

• The MDM ensures a minimum price. Even in the event that 100% of ANA tokens are sold back to the protocol.

  The MDM is how Nirvana owns the liquidity for the ANA token. The floor price of ANA is nothing other than permanently locked liquidity backing the token at a price that can only rise.

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Key components of the MDM

The Nirvana MDM is used for the purchase and sale of ANA. It transparently and algorithmically prices ANA based on its supply, and stores the liquidity used for the sale of ANA back to the MDM.

1. Supply: The total number of ANA tokens in circulation. There are no ANA tokens held in private accounts or on a distribution schedule. The entire supply of ANA must be minted, one token at a time, through the MDM.
2. Price Function: A mathematical formula that determines the price of a token based on the current supply. The Nirvana pricing function includes a hard floor - it does not go to zero.
3. Reserve: A pool of assets (e.g., stablecoins like USDC) that backs ANA and facilitates their purchase and sale. Nirvana reserves are backed by a single asset.

The price function is a multi-segment linear system of functions. It is defined by 3 lines, each taking the supply of ANA as the x-value and the price of ANA as the dependent y-value.

$$P(S) = \begin{cases} f & 0 < S < S_1 \\ b_1 + m_1 S & S_1 <= S < S_2 \\ b_2 + m_2 S & S >= S_2 \end{cases}$$

Where:

• $f$ is the floor price
• $S_1$ is the first supply threshold
• $S_2$ is the second supply threshold

The three lines are contiguous, such that the price function is continuous over the entire range of supply. Due to the required geometry of the curve, the value $m_2$ must have a shallower slope than $m_1$.

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Liquidity depth and price impact

The ANA price curve is designed for long-term stability and liquidity. It achieves this goal by increasing the liquidity for ANA as the price increases. This necessary and automatic increase in liquidity depth helps prevent crashes to the price.

The price function is a linear system over the supply of ANA. As the supply increases, so does the price. This model makes for a perfectly transparent and predictable price function. There is never a liqudity crisis for ANA. The price impact is hard-coded and a permanent feature of the market regardless of the demand for ANA.

The price impact function is constant, but it is itself a function of the supply. As the price of ANA increases, the market’s price impact decreases - which is to say liquidity depth increases. At higher prices, it takes more capital to move the price of ANA up or down a relative percantage.

To take a concrete example, suppose the slope $m_2$ is 1 / 100,000. This means that ANA will increase 1 unit of value every 100,000 tokens that are purchased. Suppose the current price of ANA is 1 USDC and the supply is 0. After 100,000 tokens are purchased, the price will be 2 USDC. After another 100,000 tokens are purchased, the price will be 3 USDC. Note that the first 100,000 units of ANA purchased moved the price up 100%. The next batch of 100,000 tokens moved the price 50% (from 2 to 3). As ANA continues to appreciate, it will take more and more capital to move the price up or down.

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Floor rising mechanism

The floor price of ANA is guaranteed due to the protocol owned liquidity kept in reserve by the MDM. The floor is the minimum guaranteed price for all ANA tokens. When the liquidity in the reserve exceeds a defined threshold, the floor price for all ANA tokens can rise.

The floor always rises by exactly 1% of its current value.

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Triggers for automatic floor rising

The floor price can rise if there is sufficient liquidity in the reserve for a recalibration of the price function with a higher floor for all tokens, while still preserving the guaranteed liquidity. There are several additional conditions which govern whether the floor actually rises when it exceeds this liquidity threshold.

1. Governance: The floor will only rise if the current votes on the floor are in the majority to raise it. If there is a majority vote to keep the floor the same, it will not rise.
2. Cooldown time: The floor will not rise if it has risen in the previous 2 hours. This cooldown prevents the floor from rising too quickly.
3. Price: The floor will only rise if the supply of ANA is beyond $S_2$ by a sufficient threshold.

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Visualizing the rising floor

The market is able to guarantee a floor price for all ANA tokens due to the fact that it automatically holds liquidity in reserve. Whenever an ANA token is purchased through the market, the assets spent on the token go into the reserve, which then get used in the event of ANA being sold back to the market.

The market pricing function operates on simple principles:

1. Every purchase of ANA moves the price upwards
2. Every sale of ANA moves the price downwards (until the price hits the floor)

As more ANA gets purchased, the token itself becomes more expensive, and more liquidity goes into the reserve. After a critical threshold of liquidity is exceeded, the automated pricing function for the market re-calibrates itself so that the floor price raises for all tokens. This is a simple redeployment of the same reserve liquidity across a new price function with a higher floor price.

The price curve itself can be visualized as line plotting the relationship between supply of ANA and the price of ANA. As the supply increases, so does the price. When ANA is sold back, its supply decreases, as does its price, until the supply hits the floor region of the price curve. When the floor rises, the line is gets recalibrated so that the floor region is higher while preserving the area under the line (which is the amount of liquidity required to back all sales of ANA).

A visual example of two price curves with different floor prices:

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Mathematical explanation

The integral under the price curve is the total liquidity in the reserve. The y-value of the price curve is the price of ANA at that supply, and when ANA is sold back to the market, the liquidity is redeemed from the reserve at the price of the curve at that supply.

Thus, when the price curve is recalibrated, the integral under the curve must remain the same. The area of the curve can be calculated by integrating the function over the interval of supply, and setting the area equal to the total liquidity in the reserve.

Since the floor price rises by 1% when the curve is recalibrated, the area under the new floor region must “move” from elsewhere in the curve. The trade-off is that liquidity is de-allocated from the regions with positive slope ($S >= S_1$) and allocated to the new floor region.

When the price curve is recalibrated, the values $m_1$ and $m_2$ (the slopes of the price curve) are preserved. This preserves the price impact of ANA before and after the floor rises. Essentially all that changes are the values of $b_1$ and $b_2$, which represent the y-intercepts the two positive-slope segments of the price curve.