# Stability management

## 1. Price fluctuation buffer mechanism

### 1.1 Design philosophy

The current crypto pledged stablecoin lacks a mechanism to adjust the closing and collateralization operations based on volatility indicators, which makes the stablecoin system unable to effectively cushion the impact of market fluctuations on pledged assets in the face of extreme market conditions, and prone to pledged asset losses in the face of a similar market crash to the one on March 12, 2020, thus affecting the balance of the entire stablecoin system.

Therefore, in designing the QIAN system, we considered the impact of price, volatility, and time on the underlying reserve assets in a comprehensive manner. Also, unlike traditional financial products, such as options, where volatility factors directly affect pricing and trading model, the QIAN Stablecoin system introduces a volatility parameter that is designed to make the equilibrium of the stablecoin less perturbed by the price of the underlying asset, thus it maximizes the ability to maintain the overall balance of the system.

### 1.2 Volatility index

QIAN V1 will introduce the Volatility Index $V_i$ as an important measure of the volatility of the underlying reserve assets.

The price of any asset goes up and down, and when the price accelerates up or down, as the return accelerates up or down, the insufficient risk of the underlying reserve asset gradually accumulates as $V_i$increases. At this time, the safety of the underlying reserve assets can be effectively cushioned from price fluctuations by increasing the initial guarantee ratio $Q_i$ and suspending liquidation operations.

As the rate of change in the price of the underlying reserve asset of the stablecoin is stabilizing, at which index $V_i$ falls and insufficient risk is released, the QUSD price from which the deviation occurred can be returned by reducing $Q_i$ and resuming liquidation operations.

### 1.3 Volatility calculations

**1.3.1 **RealVol Daily Formula

**1.3.1**RealVol Daily Formula

In traditional derivatives markets, the yield, or Realized Volatility (RealVol), especially on a daily basis, has been widely accepted as the underlying calculation parameters for a volatility index (e.g. RVOL and RVOV, etc.). Due to the unique nature of cryptocurrency trading, the traditional RealVol Daily formula for the market needs to be redesigned as the underlying parameter for the volatility calculation of stablecoin reserve asset $i$.

The RealVol Daily Formula starts with the traditional formula for standard deviation and modifies it in a few key ways:

**Annualization Factor**

RealVol sets the annualization factor to a constant. Due to the $7×24$ nature of trading in the cryptocurrency market, the actual number of trading days should be corrected to the number of days in the natural year. Since there is variation in the number of days in a month, it is better to have an approximate constant than to have several exact but different values. The constant value of 365 represents the number of trading days in a typical year. Because of the changes in the calendar in any particular year and/or the holiday schedules in any particular country, the actual number of trading days may be slightly higher or lower than 365.

**More readable representation**

The result of RealVol is typically a value less than 1.00. RealVol multiplies the result by 100 in order to bring the values to a more intuitive “fiat currency valuation” construct.

For example, the annualized realized volatility of a cryptocurrency’s return may be 0.20. Often, traders would quote this number as 20%. RealVol would disseminate the index value as 20.00.

**RealVol Daily Formula**

Where:

$R_t$ = continuously compounded daily returns from t-1 to t

ln = natural logarithm

$P_t$ = underlying Reference Price (“closing price”, determined by oracle price source) at day t

$P_{t-1}$ = underlying Reference Price (“closing price”, determined by oracle price source) at day immediately preceding day t

Where:

Vol = realized volatility

360 = a constant representing the approximate number of trading days in a year

t = a counter representing each trading day

n = number of trading days in the measurement time frame

$R_t$ = continuously compounded daily returns as calculated by formula

**1.3.2 **Design of RealVol Real-Time Formula

**1.3.2**Design of RealVol Real-Time Formula

Due to the continuous trading nature of cryptocurrencies, after deriving the daily RealVol, we need to further calculate the real-time RealVol, which provides an indication of the 1-month daily realized volatility index throughout the trading day.

All of the design elements described for the RealVol Daily Formula are the same for the RealVol Real-Time Formula. To convert from a daily to a real-time value, one needs to start with the RealVol Daily Formula, then incorporate the current underlying price and a weighting scheme. Doing so provides continuous updates throughout the trading day and delivers to traders a useful, real-time indication of the up-to-the-moment 30-day daily realized volatility. Essentially, VOL measures a constant 30-day realized volatility even while we are within the new, most recent, day (“Today”).

For instance, if we are 80% through the current day (n+1), we will use the most up-to-the-moment URP to calculate the partial (80%) day’s return (n+1) from yesterday’s URP (n). Then we consider the very first day in the calculation period and weight that whole day’s return by 20% (100% - 80% = 20%). In this manner, we still have the weight of 30-day realized volatility at any moment in time even though there are actually 31 returns — 20% weight on day 1, 80% weight on day 31, and full weights for days 2 through 30 (for a total weight of 30 days of returns).

Note: While the partial return of the current day is self-weighting, and therefore requires no additional coefficient, the self-weighted portion of the current day is nonetheless required to be calculated so as to apply the proper remaining weight to the full day 1 return. In order to calculate the weight of the current day, the current time each day is measured to the closest minute. Since there are 1,440 minutes in a day, the current time and the number of minutes in a day are used in the RealVol Real-Time Formula to calculate the daily weight to be applied to day 1.

When the time of day equals the close of today (n+1), the weight of the return of day n+1 is now 100%, while the weight of the return of day 1 is 0%. Thus, with its weight of zero, the return of the original day 1 drops out of the calculation. The original day 2 now becomes the new day 1 and all other days get renumbered as well. The RealVol Real-Time Formula at this very instant in time (the close at 12:00 PM CST in our example) simplifies to the RealVol Daily Formula. The instant after the market closes, we begin anew, with the returns renumbered, such that there are again only 30 returns, with the new trading day having a weighted return as day 31.

**1.3.3 RealVol Real-Time Formula**

Where:

1,440 = number of minutes in a day

n+1 = current today

m = number of minutes up to the current moment in time of the current day (n+1) beginning from the time of the most recent market close (day n)

$R_1$ = return for first day (day 1) of the period (from close day zero to close day 1)

$R_{n+1}$ = partial return (the return using the current underlying price and the Underlying Reference Price of the prior day).

**1.3.4 Relationship between the initial guarantee ratio **$Q_{i,0}$ and** **$Vol_{i,R}$

If $Q_i$ is always kept at a fixed value (e.g. 150%) without any adjusting factor, then in the event of market volatility, the newly minting user will be exposed to a great degree of risk, here with a real-time volatility factor, we can relate the change in real-time volatility to the initial guarantee ratio as follows:

Where:

n = current time

i = specific asset classes, such as ETH

$Vol_{R,i,n}$ = real-time volatility of asset $i$ at the current sampling point

$Vol_{R,i,n-1}$ = real-time volatility of asset $i$ at the previous sampling point

The purpose of this automated reconciliation mechanism is to find an optimal balance between user asset utilization and liquidation risk. The above equation reflects the variation of the volatility itself, and its adjustment to $Q_{i,0}$. We will continue to test this formula through the operation of the QIAN system, and as data accumulates, the reconciliation formula will also be iteratively upgraded. If deficiencies are identified in the above formula, QIAN stablecoin governance committee reserves the possibility of revising it through the community governance process.

## 2. Cryptocurrency smooth arbitrage liquidation mechanism

The QIAN system will decide whether to open the arbitrage mechanism based on the value of $Vol_R$. The system encourages liquidation at lower market volatility to mitigate the impact of short-term market panic on the stability of the QIAN system.

At any time t(i), for the guarantee rate $Q_{i,t}$, the QIAN system will have the following CSA status:

CSA(normal), where $Q_{i,t}＞Q_{i,alarm}$

CSA(alarm), where $Q_{i,min}＜Q_{i,t}≤Q_{i,alarm}$

CSA(frozen), where $Q_{i,t}≤Q_{i,min}$

For arbitragers who do not hold CSA, their redemptions may result in a reduction in the locked-in assets of CSA holders. In order to balance fairness and efficiency, for a participant of smooth arbitrage liquidation, the source of its redeemable assets at moment t(i) will be restricted to CSA(frozen).

In the arbitrage process, the arbitrager will arbitrage from the overall frozen assets of reserve asset $i$, specifically, assuming that at moment t, the QIAN system has 100 CSAs in the frozen state and these CSA generated a total of 100,000 QUSD. Any n arbitragers may use a total of 100,000 QUSD as the liquidation funds, according to the number of their contributions, receive part or all of the frozen assets from the liquidation contract. During the liquidation process, all CSA(frozen) holders will receive a share of the loss of the frozen assets as a percentage in proportion to their total assets of the frozen assets.

All reserve assets that are in CSA(frozen) can be redeemed by arbitragers, in order to protect themselves from losses. CSA(frozen) holders must be the first to replenish the reserve assets in their CSAs to get them out of the frozen state. Either the arbitragers' redemption operation or the CSA(frozen) holders' replenishment can effectively enhance QUSD's asset reserve guarantee ratio, which helps QUSD to regain intrinsic value as quickly as possible in the event of reserve assets shortage.

This liquidation mechanism is designed to encourage all CSA(frozen) holders to replenish reserve assets, but also smooth the speed and volume of liquidation of frozen assets, mitigate and reduce the losses suffered by individual users as much as possible, therefore, we named this mechanism smooth arbitrage liquidation.

Theoretically, an arbitrager could redeem any of the system's reserve assets that qualified for liquidation, and there would be no liquidation sequence of precedence among the reserve assets. The system dynamically presents the redeemable amount of each crypto-asset in real-time when arbitragers redeem crypto-assets. Redemption of cryptocurrencies by arbitrager within the range of the redeemable amount will not significantly change the distribution of cryptocurrencies across the system.

The redeemable amount of each cryptocurrency is always in dynamic change. When the reserve asset $i$ has reached the maximum redemption ratio $R_i$, which objectively raises the overall reserve guarantee ratio of the system, at this time the arbitrage operation of reserve asset $i$ is affected by the maximum redemption volume and suspended. However, as QIAN is a multi-asset system, arbitrage activities on other reserve assets will continue.

## 3. Debt auction

In extreme cases, the system's global asset guarantee ratio $Q_{total}$ may be less than 100%, if market emotion remains depressed, the arbitrage liquidation will likely be suppressed, and the arbitragers will not be sufficiently willing to arbitrage. At this moment, the system's reserve assets are undervalued and will generate an overall debt. In order to maintain the intrinsic value of QIAN, the system will unlock governance token KUN and initiate a debt auction. This will make up for the deficiency in the overall reserve assets, which will bring the overall guarantee ratio back above the safety line and restore the intrinsic value of QUSD under extreme market conditions.

For participants in debt auctions, the attraction is that the unlocked KUN tokens could be purchased below the market price. In the QIAN debt auction, the maximum discount rate Δr is introduced. Δr is initially set at a discount of 70%, but the exact value could be adjusted by vote after full community discussion. The total KUN tokens participating in the debt auction are:

Starting bids in KUN's auction

The auction participant quotes and settles the bid with asset $i$. The final price $i(final)$ is:

Assets $i$ from the auction will be used to cover the deficiency in system debt, and if there is a surplus, it will be locked into an auction surplus contract for future needs.

## 4. Global liquidation

While we holding a long-term bullish view on cryptocurrencies, we must also address the fact that cryptocurrencies are still in their early development stage, with extreme market ups and downs occurring regularly, and a multi-year bear market in the past market record.

Although the QIAN stablecoin system has a series of stabilization mechanisms, it is still possible that in the event of market extremes and the long-term bear market, even debt auction could not compensate for the system-wide reserve asset guarantee ratio. If this happens and continues for a period, it means that the entire QIAN stablecoin system permanently loses its intrinsic value support. We will explore whether to conduct a global liquidation and shut down the QIAN stablecoin system in this case through a community governance process. Once the community governance passes the proposal to close the QIAN stablecoin system, a global liquidation will be initiated.

In the global liquidation state, the system will first freeze all CSAs and disable CSA generation, followed by terminating the price feed oracle and use the price of the last price feed oracle as the reference quote for the system's global liquidation. At this point, the system state changes again and users holding CSA(normal) have priority to redeem their locked assets from CSA(Normal) contract, the system will process the asset redemptions for this group of users. After the completion of asset redemption for all CSA(normal) holding users, if there are still reserve assets remaining in the system, the redemption of CSA(alarm) will initiate.

In the global liquidation state, it is uncertain whether the user will be able to get back all of the locked assets without suffering a loss. The probability of being able to redeem the locked assets in full is in order of $CSA(normal) > CSA(alarm)$. The amount of various underlying reserve assets, market price, and other factors can have a combined effect on the probability of a successful redemption.

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