pip install -r requirements.txt
jupyter notebook
python main.py python main.py --flagfile=tests/su_black_swan.txt
Stable Unit (SU) is a digital token designed to maintain a 1:1 peg to the US dollar. The system will be fully decentralized --running via smart contract on a Bitcoin side chain-- and have its stability maintained using a non-fiat reserve. The contract begins with a market cap which is fully collateralized by its Bitcoin reserve but eventually transitions into a highly liquid system dependent on bonds as its market grows.
Demand for Stable Units is likely to vary widely when the network is small. At this stage we keep the system risk low by guaranteeing the redemption of Stable Units for bitcoin held in reserve at a 1:1 ratio.
The contract maintains liquidity around the dollar peg by offering SU to sellers and buyers through its main contract. We parametrize this mechanism with a delta offset from the peg -- buyers can attain SU through the contract at a price greater than a dollar and redeem them through the contract at a price lower than a dollar.
In effect, the contract acts as a market maker, which can adjust it's risk by adjusting the spread between the lowest bid and highest ask. As prices rise and fall on the exterior market the contract profits. During periods of high volatility, revenue from this bid/ask spread is deposited into contract's reserve, elevating its value and allowing the token contract to expand further at a constant reserve ratio.
In the beginning, while the Stable Unit economy is small, the price band (spread) surrounding the stable price is tight and the contract is fully backed at target reserve ratio of 1:1. This effectively shields the contract from risk but limits the possible quantity of Stable Units in incirculation. As the market grows however, the reserve ratio decreases and the the bid-ask spread is allowed to increases in width. In effect the contract can maintain a larger market value while still affording strong protection to the underlying reserve.
This mechanism itself has risks which is why we employ additional stabalization mechanisms which come into play once the first stop gap has been broken. Although these methods are not tested here, the real contract will employ selling of bonds, fund parking, and share dilution to maintain the contract health.
The Bitcoin reserve is itself subject to it's own risk, and the overarching goal of the Stable Unit token is to remove all dependences on secondary markets. Because of this, as the system grows, we reduce the dependence of Stable Units on reserve backing, and instead, open up a secondary market for bonds.
We simulate the behaviour of this contract useing two non-correlated Geometric Brownian Motion timeseries:
- The Bitcoin price and,
- The demand for Stable Units on exterior markets.
The first of these series, the bitcoin price, is required in this simulation because it is being held by the contract reserve --used as the method of exchange. Its price with respect to the peg, i.e the BTC/USD, must be derived using oracles to determine the bid and ask prices offered by the contract.
We use the standard GBM model with gaussian Wiener process. At each step we derive the next price using the following GBM step rule:
dS_{t}=\mu S_{t}\,dt+\sigma S_{t}\,dW_{t}
Additional random walk distributions such as fractional Brownian motion (fBm) could be used intead of this simple gaussian Wiener process. For simplicity we use this model parameterized by it's dt, sigma and mu. Choices for these parameters are made by fitting this motion to the historical bitcoin price movement. We can additionally select mu (its drift term) to match either an upward or downward trend in the Bitcoin price.
Unlike the Bitcoin price, we model the Stable Unit demand, which reflects the quantity of Stable Units being demanded on exterior markets. This is more relevant to the contract behaviour because it must engage with exterior markets by buying and selling Stable Units are the contract bid and ask prices.
Again we use the standard GBM model and a gaussian Wiener process to model demand changes.
The two motions interact with the contract according to the following rules:
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When the Stable Unit demand increases on exterior markets, this reflects a price drop which increases above the lowest ask price offered by the contract. Traders sell Stable Units on exchanges and buy more from the contract to equalize the price.
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When the demand for Stable Units drop on exterior markets the price drops bellow the highest bid offered by the contract. Traders buy Stable Units on exchanges and sell them to the contract to bring the price up.
When the ratio between SU and BTC held in reserve drops below a threshold value we consider this a failure. By running multiple trials and evalutating the outcomes statististically, we can probabilistically measure the risks to the system.
Monte Carlo methods are common place tools in statistical finance which allow researchers to make empirical estimations of systemic risk, under specific assumptions about the movement and relationships between key system components.
In our case, Risk to the Stable Unit system can be understood as the likelyhood of the contract reserve ratio dropping bellow an undesirable threshold.
We derive estimates of this risk through repeatedly simulating the behaviour of the contract and recording samples. Aggregations of these samples give us an outcome distribution from which we can derive statistics. For instance, 'Given our assumptions about the behaviour of the Bitcoin price, and Stable Unit demand, there is a 90% chance that the contract reserve ratio will remain above above 0.5 within a years time.
It should be noted that there is no perfect method for assessing the risk to financial instruments. Financial data it notorious random and subject to black swan events as a consquence of price distributions which are long tailed and unknown. For the purposes of testing the behaviour of this system, however, Monte Carlo methods serve as usefull way of understanding the different dynamics that may appear and making rough estimations of risk.