Predicting ETH Volatility Using Squeeth 0x358c
May 30th, 2022

Squeeth is a new DeFi product released by Opyn in January. As the first on-chain power perpetual, Squeeth is similar to an option without an expiry date or a strike price. In addition to increasing liquidity in the options market, some have suggested that Squeeth can be used to hedge Uniswap LPs, hedge all ETH/USD options, and predict the volatility of ETH in the short term. This piece will investigate whether Squeeth adequately serves this purpose.

### Different Types of Volatility

Before we analyze how effective the price of Squeeth is in predicting the future volatility of ETH, we should describe which metric is the most accurate in measuring volatility.

Volatility is defined as the dispersion of price of a given stock. In other words, the more volatile a stock is, the riskier an investment in that stock becomes. If the volatility of a given stock is high, then traders should expect the prices of that stock to fluctuate greatly in value. In traditional finance, there are several ways to measure the volatility of a given stock.

The most common ways that volatility is measured is using either standard deviation or variance. This way of quantifying volatility makes sense as the standard deviation of historical prices of a stock measures the fluctuations and deviations from the average price of the stock: the greater the standard deviation of the prices, the greater the historical prices have moved up or down from the mean. Assuming that the prices of a stock are distributed in a normal distribution, traders can infer that around 68% of all prices of the stock fall within one standard deviation of the mean. Therefore, given the standard deviation as a measure of volatility, traders can make a quantifiable estimate as to the possible region that the price of the stock will be in the future. This type of volatility is called realized volatility.

Another method of quantifying volatility is to use the beta(ß) of a stock. The beta works by comparing the volatility of the stock to the volatility of another benchmark stock, commonly the S&P 500. In order to calculate the beta of stock A by comparing to the benchmark stock B, we use the following equation:

In which R_A represents the returns on stock A and R_B represents the returns on stock B. The way that a beta is interpreted is that if β=0.5, stock A is half as volatile as stock B. So, if beta is greater than 1, stock A is more volatile than stock B. If beta is less than 1, stock A is less volatile than stock B. If beta is equal to 1, then the volatility of stock A and stock B are equal.

Options can also be a good measure of volatility. The price of options can be used to calculate something called implied volatility. Unlike the other two methods, implied volatility does not directly predict the price fluctuations of a stock, but instead estimates the overall sentiment of traders in the options market of how a stock’s price will fluctuate. This is because the price of an option in the market increases if the volatility of the stock rises, as options are more in demand to hedge stocks if the stocks are riskier. The implied volatility is usually calculated using whichever way that the option premium is calculated, usually using the Black Scholes Equation.

In our investigation of how good the price of Squeeth is at predicting the volatility of ETH, we shall look at standard deviation only, as standard deviation is the easiest to interpret.

### Results

As we have discussed above, we will be comparing the prices of Squeeth to the past realized volatility of ETH prices to analyze how well prices of Squeeth predict volatility. Fig. 1: Chart displaying the price of Squeeth compared to the realized volatility of the price of ETH

Fig. 1 above displays the price of Squeeth compared to the realized volatility of the price of ETH up until that same time point. What this means is that we are analyzing how well the price of Squeeth predicts an indicator of historical volatility, or the volatility of the price of ETH up until the current time point. The past realized volatility, or the standard deviation, is calculated from the start of when Squeeth was released to the current time point depending on the time point of a particular price of Squeeth. From the data above, we have calculated a polynomial trendline with an equation that can help us predict the realized volatility of the price of ETH given the price of Squeeth, which is as follows:

This trend line does fall in with our expectation that an increase in the price of Squeeth follows an increase in the volatility of ETH. This is because when the price of ETH becomes more volatile, the demand for options to hedge the price of ETH increases, leading to an increase in the price of Squeeth. Additionally, the trend line is polynomial because the price of Squeeth tracks the price of ETH^2. However, this trend line only has a coefficient of determination (R^2) of 0.642. This means that there are a lot of outliers in the datapoints that we have analyzed, so we cannot use the equation above to calculate with absolute certainty what the volatility of ETH is in the current moment given the price of Squeeth. Fig. 2: Chart displaying the price of Squeeth and the realized volatility of the price of ETH since the release of Squeeth

From Fig.2, which displays the price of Squeeth and the realized volatility of the price of ETH since late February, we can see that the price of Squeeth somewhat tracks the relative volatility in the price of ETH. The correlation coefficient of the two data sets over the time period in the chart above is 0.993, which indicates an extremely positive correlation.

The realized volatility, or the standard deviation, is calculated by taking the sum of the differences of each data point from the mean of the sample. We shall also analyze how this difference can be predicted as well. Fig. 3: Chart displaying the price of Squeeth compared to the absolute difference from mean of ETH prices

Fig. 3 above displays the price of Squeeth in the x-axis compared to the absolute difference between the price of ETH at the same time point and the mean of the price of ETH over the period of time since Squeeth was released. From the chart, we can see that the difference between the price of ETH and the average price of ETH can be predicted accurately using difference equations depending on whether the price of Squeeth is above its average. The equations are as follows: if the price of Squeeth is below the average (\$727.07), the equation used to predict the difference is

If the price of Squeeth is above the average (\$727.07), the equation used to predict the difference is

For the difference when the price of Squeeth is below average, the trend line with the equation given above has a coefficient of determination (R^2) of 0.963. For the difference when the price of Squeeth is above average, the trend line given above has a coefficient of determination of 0.961. These values are both significantly high, which indicates that the price of Squeeth is greatly correlated with the difference of the price of ETH from its average. What this implies is that the price of Squeeth is an effective predictor for how much ETH deviates from its average, which essentially quantifies the volatility of ETH. Using difference equations given whether the price of Squeeth is above or below average, we can predict how much risk the price of ETH exposes us to.

### Conclusion

From our investigation into how Squeeth tracks the volatility of ETH, we have found that there is a polynomial relationship between the price of Squeeth and the realized volatility in the price of ETH up until the same time point. This is an indication of how well Squeeth tracks the historical volatility of ETH. The price of Squeeth and the realized volatility in the price of ETH are also positively correlated. Finally, we have found that the price of Squeeth is a good predictor for how far the price of ETH has deviated from its mean.

The implications of the findings in this piece is that traders should use Squeeth as a strong indicator for the volatility of ETH going forward. Squeeth is a similar predictor for the volatility of ETH to the VIX (CBOE Volatility Index), which predicts the volatility of the S&P 500 index using option prices. Squeeth is different to the VIX in that Squeeth does not have an expiration date and VIX relies on options with expiration dates in the near future (within 30 days). Whether or not this difference makes Squeeth more reliable has not been investigated in the scope of this paper.

In addition, Squeeth is an alternative to any USD/ETH option as there is exposure to pure convexity and there are no expiration dates or strike prices. However, it is important to note that traders who are long Squeeth have to pay a daily funding rate to make up for this constant exposure to decreased risk and increased reward.

About the author: Shelly Liu is a rising junior at Harvard College studying computer science. She is currently an intern at Google working in software engineering.

Special thanks to Zubin Koticha for his guidance and thoughtful feedback in the process of producing this piece.

Disclaimer: Harvard Blockchain and the author of this piece are not financial advisors. Nothing contained in this research piece should be construed as investment advice.

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