Peercoin Stabilization/Counterparty Asset

Nu Economics
The economic model of Nu is based on the concept of a virtual price ($1) and an actual price. When the actual price is under $1, sell NSR and buy NBT. When the actual price is over $1, sell NBT and buy NSR. Since neither the NSR nor the NBT supplies are fixed or follow any specific fair distribution mechanism these actions can be done at will using any 3rd party exchange or escrow.

Fair Distribution
If we take one of the tokens to have a supply dependent on complex factors the economics looks a little different. In this case we are forced to acknowledge the asymmetry and call the two tokens the ‘asset’ with inflatable supply and the ‘coin’ with externally determined supply. When the actual coin price is under the virtual coin price (the coin value is falling) then assets can be sold at will. However, when the actual coin price is above the virtual coin price (the coin value is increasing) we cannot inflate coin supply beyond the amount of coins gained from previous asset inflation and we cannot deflate asset supply below the base number of holders (people who will never sell, or lost the keys). Still, if we stabilize the virtual asset price with respect to the coin then adjusting the virtual asset/coin price will give leverage over the actual coin price via the actual asset price.

Opportunistic Distribution
The only purpose of the asset is to act as a counterparty for the coin, so its only target audience is traders. On a flat PPC day, the asset will be traded 1:1 with PPC (at some offset) from supply. When PPC goes up, one asset token may go for 1.05 PPC. When PPC goes down, the same asset could go for 0.995 PPC. As the asset can only be traded from supply for PPC (not BTC or USD) this gives traders an incentive to give up their PPC for assets instead of selling it on the market. Then, when PPC is more profitable the asset will pay out. This can be described using a positive change factor Q with Q=1 representing a flat market.

The Singularity
If the fund contains no money, then someone buys 1 asset for 1 ppc, then sells it again when ppc goes down then the fund cannot give more money than it has. During a bank run, the virtual asset to coin price (VACP) is determined as follows:
and VACP = Q otherwise
where CF is the number of coins in the coin fund and AS is the asset supply.

Historical Price
An attempt at producing a Q that will stabilize the coin price uses the difference between the virtual coin price and the actual coin price, then determines the virtual coin price using trading tools like an estimated moving average (EMA) to produce a stable target price. In this way, the virtual coin price can be seen as a historical price while the actual price is the most recent price, or an EMA with a much shorter averaging window.

Structural requirements
The issuer would need to automate the issuing of assets for coins and vice versa. Q would need to be actively determined using API commands or a blockchain service like PeerTicker. The issuer can take a small slice from each transaction, and of course the fundamental peercoin fee would be charged to each transaction.

To avoid extreme manipulation of the system, something like a limit on how many assets can be bought or sold in an hour would be appropriate. This would help to prevent very short term manipulations of ppc to trade large amounts of the asset.

The singularity is actually much more complicated than this, as the price must be such that it never pays out more than it has even for someone selling the whole asset supply with infinite Q. Anyway, this is just the basic idea, not a full technical writeup.