**Design Concept**

The current mainstream cryptocurrency-backedstablecoins for stakinglack a mechanism to adjust close out and collateral operations according to volatility indicators. As a result, when extreme market conditions come, the stablecoin system cannot effectively buffer the impact of market fluctuations on the staked assets. In face of price plummeting as what happened on March 12, 2014, staked assets are likely to suffer losses, which will affect the balance of the entire stablecoin system.

Therefore, when designing the QIAN system, we comprehensively considered the impact of price, volatility, time, etc. on the underlying reserve assets. The introduction of volatility ratio index to the QIAN stablecoin system aims to reduce the disturbance of asset prices to the stability of the stablecoin, so as to maximize the overall balance of the system.

**VolatilityRatio Index**

QIAN will introduce the volatility index Vias a key indicator to measure the volatility of the underlying reserve assets. Every cryptocurrency changes in price, and when the price rises or falls faster, the Vi of the underlying reserve asset of the stablecoin increases, so does the risk of staking, as the rate of return accelerates to go up or down. Now, by increasing the start adequacy ratio Qi,0and postponing liquidating, the impact of price fluctuations on the security of the underlying reserve assets can be effectively buffered. When the price of the underlying reserve assets becomes stable,Vdrops and the risk to stake is released. By reducing Qi,0and resuming the liquidating, the deviated price of QIAN can go back to normal.

**Daily RealVol**

In the traditional derivatives market, the rate of return, or Realized Volatility (RealVol), especially the daily RealVol, has been widely accepted and used as the basic calculation parameter for option volatility indexes (such as RVOL and RVOV, etc.). Due to the particularity of cryptocurrency trading, the daily RealVol formula for the traditional market needs to be redesigned to serve as a basic parameter to calculate the volatility of the stablecoin’s reserve asset i.

The daily RealVol formula starts with the traditional standard deviation formula and has been modified in several key aspects:

**Annual coefficient: **RealVol sets the annual coefficient to a constant. Since the crypto market has trading conducted 24/7, the actual number of trading days should be changed to the day number of a natural year. Because of changes in the day number in the month, it is better to have an approximate constant, rather than several exact but different values, so we set the annual coefficient to 360 at the beginning of the system.

**A simpler representation: **The result of RealVol is usually a value less than 1.00. So we choose to multiply the RealVol result by 100 to achieve a simpler representation. For example, the annual RealVol for a cryptocurrency may be 0.20. Normally, we would multiply this value by 100 and represent it as 20.00.

**Daily RealVol Formula**

Rt= Continuously Compounded Return from t-1 to t

ln= Natural logarithm

Pt= The benchmark price at t (time) on the current day ("closing price", the specific time is determined by the oracle’s quote source)

Pt-1= The benchmark price on the day before t ("closing price", the specific time is determined by the oracle’s quote source)

Vol = Daily Realized Volatility

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

t = the count for each trading day

n = number of trading days in a time frame

Rt = Rate of continuously compounded return calculated by the formula.

**RealVol Formular**

Cryptocurrencies are traded constantly, we need to calculate the real-time RealVol based on the daily RealVol. We will calculate the real-time RealVol on a 30-day cycle.

All factors involved in the daily RealVol formula are the same as the real-time RealVol formula. To convert daily values to real-time values, we need to start with the daily RealVol formula and take the current base price and weighting plan into consideration. This can provide continuous updates throughout the trading day and provide useful real-time instructions to CSA holders to understand the daily RealVol in the next 30 days. Essentially, the 30-day constant RealVol can be measured when we are at any moment of the day (today).

For example, if the trading hour percentage on day n+1has passed 80%, we will use the latest underlying real-time price (URP) and yesterday’s corresponding URP (80%) , to get the return for today (n + 1). Then, we will take the first day of the calculation period and weigh the rate of return on that day by 20% (100%-80% = 20%). In this way, we can still get the weight of the RealVol achieved at any point within 30 days, even if there are actually 31 returns. The weight of the 1st day and 31st day are 20% and 80% respectively, and that of the remaining days is 100%.

Note: Although the partial return for the day is self-weighted, hence no additional synergy factor is required, it is still necessary to calculate the self-weighted part of the day in order to apply an appropriate residual weight to the full-day return on the 1st day. In order to calculate the weight of the day, the nearest minute of the day should be taken. Since there are 1,440 minutes in a day, the current and the second counts in a day will be applied to the weight of the 1st day in real-time RealVol formula.

When the time of n+1 day is the closing time, the weight of the n+1 day is 100%, and the weight of the 1st day is 0%. Therefore, since its weight is 0, the rate of return on day 1 is deleted from the calculation. The original day 2 is now day 1, and all other days are renumbered. The real-time RealVol formula is simplified to the daily RealVol formula at this point (in our example, the market closes at 0 o’clock, China Standard Timeevery day). The moment after the market closes, a new trading day begins, and the rate of return is renumbered, so that there are only 30 rates of return, and the new weighted rate of return starts from the 31st day.

1,440 = minute count in a day

n+1 = today

m = the minute count from the nearest closing time on Day n to the nearest minute on Day n+1

R1= the rate of return on the 1st day in a calculation circle

Rn+1= partial returns (the return of the current related price and the related reference price on the day before)

Note: For clarification, the flower body "R" means partial returns, and all other returns are full-day returns.

**The Relationship between Start Adequacy Ratio Qi,0and Voli,R**

If there is no adjustment factor and Qi,0 is always kept at a fixed value (for example, 150%), users who open new positions will be exposed to great risks when the price is fluctuating. With real-time volatility, we can establish the following relationship between the real-time volatility change value and the start adequacy ratio:

n = the current moment

i = a certain cryptocurrency, likeEthereum

VolR,i,n= the real-time realized volatility of asset i at the current sampling point

VolR,i,n-1= the real-time realized volatility of asset i at the last sampling point

The above relationship reflects the change value of volatility itself and its adjustment effect on Qi,0. We will continue to test this formula based on the operation of the QIAN system. If the above formula is found to be inadequate, The Force Protocol team reserves the right to modify it through community governance procedures.