Market risk and volatility assessment formulas are engineered to adjust collateralization requirements dynamically to ensure a reasonable on-boarding ratio for users who want to collateralize synthetic asset pools based on the present state of the market.

Without this value being dynamic a set value creates over-collateralization, which hinders individuals from taking part in the trading of synthetic assets.

Community voting is a popular method by which a set collateralization value is calculated. However, the community at large is often unaware of the complexities involved in determining the best value. Therefore, collateralization will be determined algorithmically as a dynamic value and not a set value.

### Volatility Determination

Since most crypto assets move in parallel to Bitcoin we are able to determine the volatility drawdown for the crypto market using the following steps:

The **formula** for daily **volatility** is computed by finding out the square root of the variance of Bitcoin's daily price. Further, the annualized **volatility formula** is calculated by multiplying the daily **volatility** by a square root of 365.

** Step 1:** We first gather the daily price of Bitcoin and then determine the mean. Let us assume the daily price on an

*i*day as

^{th}*P*and the mean price as

_{i}*P*.

_{av}** Step 2:** Next, we compute the difference between each day’s Bitcoin price and the mean price, i.e.,

*P*.

_{i}– P** Step 3:** We then compute the square of all the deviations, i.e.

*(P*.

_{av}– P_{i})^{2}** Step 4:** Next, find the summation of all the squared deviations:

*$$\sum(Pav-Pi)^2$$*

** Step 5**: Next, divide the summation of all the squared deviations by the number of daily Bitcoin prices, in this instance we say n. It is called the price variance of Bitcoin.

*$$V=\sum(Pav-Pi)^2/n$$*

** Step 6:** Next we compute the daily volatility or standard deviation by calculating the square root of the variance of Bitcoin.

*$$DV = \sqrt{\frac{(Pav-Pi)^2}{n}}$$*

*DV* = Daily Volatility

** Step 7:** We annualize the volatility. The formula is calculated by multiplying the daily volatility by the square root of 365. Here, 365 is the number of active trading days in a year (crypto markets don't close as traditional markets do).

*$$AV = \sqrt{365} \frac{(Pav-Pi)^2}{n}$$*

*AV* = Annualized Volatility

### Moving Average Computation

We take the EMA for BTC/USD and analyze the short term and long term averages to create a balance for our collateralization rate.

*$$EMAt=[Vt(\frac{s}{1+d})] + EMAy[1-(\frac{s}{1+d})]$$*

**Where:**

*EMA*= EMA today_{t}*V*= Value today_{t}*EMA*= EMA yesterday_{y}*s*= Curving smoothing*d*= Number of days

We take 3 EMA data points from average cycles to cover the entire crypto landscape. Since the average cycle duration seems to be about 3 years, we have a max point to indicate the higher-end level of risk tolerance which will carry a heavier weight impact on our risk index calculation.

### MA Vs. EMA

We propose *EMA* as it emphasizes more on recent data points. Because of this, *EMA* can be considered more of a weighted average calculation.

### Weighing Importance

Sigma Risk Index output weighs every data point according to importance.