Synth Subnet Volatility Modelling Insights

Bitcoin Volatility

One of the key challenges in the Synth subnet is forecasting volatility. Having models that can distinguish between periods of high and low volatility provides miners with a significant edge, particularly when predicting assets prone to frequent price swings, such as cryptocurrencies. In this phase of the subnet, the focus is specifically on Bitcoin.

The baseline model initially recommended for forecasting Bitcoin price movements is the Geometric Brownian Motion (GBM) with fixed volatility. Volatility is estimated from historical data, and miners must determine the optimal time window for this estimation, as well as how frequently to update it.

However, miners who dynamically adjust their volatility models to changing market conditions are more likely to outperform others in the subnet. For instance, consider Bitcoin price movements from December 1, 2024, to March 25, 2025, along with its log-returns and daily volatility:

The figure illustrates frequent peaks of high volatility and periods of sustained volatility. The average daily log-returns volatility during this period was approximately 0.07%. Using this as a fixed input for the GBM model would likely result in forecasts that fail to capture significant price swings, placing miners at a disadvantage over time.

A clear example of structural volatility variation emerges when analyzing data by days of the week (Monday to Sunday) and hours of the day (0–23). The following heatmap displays the standard deviation of 1-minute net returns for Bitcoin over the same period, aggregated by weekday and hour:

The heatmap reveals how volatility fluctuates throughout the week. Monday, particularly Monday afternoon, exhibits the highest volatility. Weekday afternoons tend to be more volatile than mornings, with elevated volatility persisting into the night (until around 1–2 AM), after which it declines to the more stable morning hours. Saturdays, by contrast, appear relatively stable compared to other days. The low volatility observed on Saturdays continues through Sunday morning and early afternoon. However, by late Sunday afternoon and evening, volatility starts rising again, seemingly "preparing" for the upcoming Monday.

Miners’ Volatility Modelling: Two Case Studies

Do miners adjust their forecasts based on changing volatility patterns, or do they rely on a fixed volatility value when predicting Bitcoin prices? To investigate this, we analyzed the forecasts of two miners as follows:

• We examined the period from March 15 (when the V2 scoring system was fully implemented) to March 25.

• We aggregated the total rewards earned by miners during this period and selected the top-ranked miner and the miner ranked 100th.

• For these two miners, we analyzed the first hour of all their provided forecasts within the selected period.

• We calculated net returns from these price forecasts, grouped them by weekday and hour, and generated heatmaps.

The heatmap of the top-ranked miner demonstrates an awareness of Bitcoin’s volatility dynamics. Similar to the actual Bitcoin price, Monday exhibits higher volatility, and weekday afternoons are more volatile than mornings. Additionally, this miner effectively captures the low volatility observed on Saturdays and early Sundays (except for an anomaly on Saturday at 3 PM, possibly due to outliers).

In contrast, the heatmap of the 100th-ranked miner shows relatively fixed volatility values across all days and hours. This miner likely relies on the baseline GBM model with fixed volatility. The lack of variation in forecasted volatility places this miner at a disadvantage, reflected in their lower ranking.

Takeaways

While the GBM model with fixed volatility serves as a solid starting point, miners gain a true competitive edge by effectively modeling Bitcoin’s dynamic volatility. This report highlights one possible approach: accounting for volatility variations across different periods of the week.

However, miners can enhance their models further by incorporating additional factors such as:

• Seasonal and Cyclical Trends – Monthly patterns and broader seasonal influences.

• Volatility Clustering – Periods of high volatility followed by further high volatility, and vice versa.

• Market Regimes and Sentiment – External market conditions and investor behavior.

The core principle of the Synth subnet is the ability of miners to integrate these factors into their forecasts. Achieving this requires careful analysis and robust modeling techniques, but the rewards are substantial.

Our findings demonstrate that top-performing miners utilize more sophisticated models than the baseline GBM. The Synth subnet benefits from miners who continually refine their models, as this leads to higher-quality data for stakeholders such as liquidity providers and Automated Market Makers (AMMs). The liquidity probabilities and expected impermanent losses derived from the forecasts of top miners in the Synth subnet are likely to be more accurate than those produced by in-house models.

By striving for more precise volatility modelling, miners not only improve their own performance but also contribute to the overall robustness of the ecosystem.