NXD Protocol University
Deep Dive: Price Floor Economics
Introduction
In understanding the value proposition of NXD, it is important to understand the concept of a price floor from the perspective of Uniswap’s AMM. In this article, this concept will be outlined and integrated into NXD’s fundamental value proposition. We invite the community to read along and gain an understanding of this integration.
What… a k hole?! Understanding the “constant product” formula k of Uniswap
Uniswap is an automated liquidity protocol powered by a constant product formula and implemented in a system of non-upgradeable smart contracts on the Ethereum blockchain. Each Uniswap V2 smart contract, or pair, manages a liquidity pool made up of reserves of two ERC-20 tokens. In a traditional Uniswap LP, these tokens track pro-rata LP shares of the total reserves, and can be redeemed for the underlying assets at any time[1].
These liquidity pairs act as automated market makers, standing ready to accept one token for the other as long as the “constant product” formula is preserved. This formula, most simply expressed as x * y = k, states that trades must not change the product (k) of a pair’s reserve balances (x and y). Because k remains
unchanged from the reference frame of a trade, it is often referred to as the invariant[2].
Locked Liquidity in Uniswap’s V2 AMM
By locking liquidity, the design of the Uniswap V2 AMM generates a price floor. This means that, the token has a price floor resulting that it will never drop under a certain price even if all assets are sold into the LP. This is quite advantageous for a cryptocurrency in the DeFi space which is plagued by hyperinflating tokens.
As the team provides the initial liquidity for the NXD/DXN LP and renounces ownership of that LP, the team locks the LP and ensures that there is always a base level of liquidity available for traders and creates a floor price for NXD in DXN terms.
Requirements of a Price Floor
In the following section, we provide a short example of the prelude to the calculation of a price floor in a hypothetical scenario. The following requirements need to be present to be able to create a floor price in a UniV2 LP.
- The fact that there is a fixed supply of the token, in our case being NXD
- The fact that the contracts prevent removing liquidity from the LP, liquidity needs to be locked
- The UniswapV2 rules governing the price of a UniswapV2 trading pair being the “k” formula
Implementing the k formula
In the context of Uniswap[3], a decentralized finance protocol, the concept of a “floor price” is introduced through the application of the constant product formula, symbolized by “k”. K is the name of the mathematical product of the pooled assets within a Uniswap liquidity pool.
The Uniswap V2 algorithm will make sure k stays constant after each trade. This principle is pivotal for determining the exchange rate and price between two different tokens within the Uniswap V2 AMM.
Example of calculating “k”:
In the following example, we assume that there’s 3333 NXD and 34667 DXN inside the LP, which results in k of 115545111.
- k = <pooledNXD> * <pooledDXN>
- k = 3333 * 34667 = 115545111
Example of calculating the amount of DXN and price of NXD after an NXD trade, using “k”:
In the following example we calculate the amount of DXN and price of NXD after a trade where we sell 100 NXD into the LP. Remember that, the Uniswap V2 algorithm will make sure k stays constant after each trade.
Now we sell 100 NXD into the LP, how much DXN should be left in the LP?
- k = 115545111 and NXD = 3433 (3333+100) and DXN = x.
Now we’re solving for x:
- 115545111 = 3433 * x
- x = 115545111 / 3433 = 33657.2
Since we had 34667 DXN before the sale of 100 NXD, that must mean that we’ve got 1009.8 DXN from selling 100 NXD, as 34667–33657.2 = 1009.8.
This means that the price of NXD in the LP has changed from:
Before selling 100 NXD:
- Price NXD = 34667 / 3333 = 10.4 DXN/NXD
After selling 100 NXD:
- Price NXD = 33657.2 / 3433 = 9.8 DXN/NXD
Calculating the hypothetical Price Floor of NXD
Now, we’ve reached the thought experiment to introduce the calculation of the Price Floor of NXD.
We’ve now seen that, if 100 NXD gets sold inside the LP the price of NXD goes down in DXN terms. Now, to reach the price floor, we have to assume that all available NXD outside the LP is sold into it. This brings the price down to its mathematical floor price in DXN terms as there’s no more NXD to put inside the LP.
It is important to understand that, this situation in reality is extremely rare to exist as there will always be speculators present. A floor price doesn’t function as a technical level of downside in terms of trading, it provides functionalities that increase the fundamental value of an asset.
The fundamental value of an asset with the mathematical certainty of a floor price is that it:
- provides risk management tools for speculators and asset managers,
- grows the applicability for future dApp integrations of the underlying asset, and;
- it generates one of the hardest store of value capabilities, a floor price.
Example of calculating a Price Floor:
In our scenario, to calculate the Price Floor of NXD priced in DXN, the following applies. Again remember that, k must remain constant, and let’s say the total supply of NXD was 10,000 and everything was sold inside the LP.
First, we assign the right values to the different variables, to derive the amount of pooled DXN:
- k = 115545111
- <pooledNXD> = 10,000 (as all NXD is sold into the LP)
- <pooledDXN> = ?
- k = <pooledNXD> * <pooledDXN>
This results in the following amount of DXN inside the LP:
- <pooledDXN> = 115545111 / 10,000 = 11554.5
This means that we would have 11554.5111 DXN in the LP, and now the new price floor of NXD is simply the price of NXD in DXN terms:
- Price Floor of NXD = <pooledDXN> / <pooledNXD> = 11554.5 / 10,000 = 1.2 DXN
This means that, even if all NXD is sold inside the LP the value of each NXD equals 1.15545111 DXN and can never be lower than that.
Exponentially increasing the Price Floor by introducing Deflationary Tokenomics
The previous hypothetical example provides a base understanding of the mathematics behind a floor price of an asset. In the following graph, we’d like to show the powerful effect of combining the concept of a price floor with deflationary tokenomics.
By burning a capped supply asset and combining this with locked liquidity, the price floor of the asset gets increased with each burn, resulting in a perpetually increasing floor price that grows exponentially.
It is important to understand that, the derived price floor signifies the minimum value of NXD in DXN that can be expected, regardless of the trading volume or the number of transactions. This floor price in DXN, however, does not shield NXD from fluctuations in its fiat currency valuation, as it is tethered to the value of DXN itself. Thus, while the floor price ensures NXD’s value does not fall below a certain threshold in DXN terms, its fiat equivalent may still vary with DXN’s price movements.
Due to NXD’s fundamentals, liquidity cannot be removed, and NXD tokens cannot be minted after the Limited Mint Phase (LMP). With the launch of NXD Protocol and the LMP, the NXD Price Floor starts to increase perpetually by programmatically burning NXD through different smart contracts integrated into the NXD Protocol. In the following article, the smart contract strategies burning NXD will be outlined in further detail.
Looking Ahead
The following article will provide an overview of the value propositions of the NXD Protocol and how it combines the power of compounding with deflationary tokenomics to programmatically increase its price floor in perpetuity.
Open Source
All NXD code is published on GitHub and is audited by Arcadia.
Find Us Here
- X (Twitter): https://twitter.com/NXD_Protocol
- Telegram: https://t.me/NXD_Protocol
- GitHub: https://github.com/DXNhyperstructure/NXD-Protocol/ (private repo in audit)
DISCLAIMER: The content and materials featured related to the DXN Hyperstructure Initiative and/or NXD Protocol are for your information and education only. The information does not constitute financial advice or recommendation and should not be considered as such. Always do your own research and seek independent financial advice when required. The value of your investments and any income derived from them can fall as well as rise and you may not get back the original amount you invested.
[1] https://docs.uniswap.org/contracts/v2/concepts/protocol-overview/how-uniswap-works
[2] https://docs.uniswap.org/contracts/v2/concepts/protocol-overview/how-uniswap-works
[3] https://docs.uniswap.org/contracts/v2/concepts/protocol-overview/how-uniswap-works
