Measuring the uncertainty of NFTs through Confidence Intervals.

TL’DR: Confidence intervals provide assistance in measuring the uncertainty of assets.

The estimation of volatility for NFT (Non-Fungible Token) assets is of significant interest in the domain of financial analysis. Volatility, representing the degree of price fluctuation and uncertainty, plays a crucial role in assessing the risk and potential return associated with these unique digital assets. In this context, confidence intervals can act as a valuable tool for measuring uncertainty and establishing a range of possible outcomes.

By computing confidence intervals for NFT asset volatility, we can unlock several opportunities for analysis and decision-making. Here, we explore those opportunities in the following ways:

1. Risk Management/ Portfolio Optimization: Confidence intervals enable investors to construct portfolios with a consideration of NFT asset volatility. By accounting for the uncertainty associated with each asset, investors can seek to optimize portfolio returns while managing risk. Confidence intervals facilitate the evaluation of trade-offs between risk and reward, supporting the identification of optimal asset allocation, position sizing, and hedging techniques
2. Detailed Investment Decision-Making: By comparing confidence intervals across different NFT assets or investment opportunities, investors can make more informed investment decisions. Assets with narrower confidence intervals may indicate relatively lower volatility and potentially offer a more stable investment choice.
3. Pricing and Valuation: Confidence intervals can aid in pricing NFT assets, especially in marketplaces where transaction data is limited or volatile. By incorporating confidence intervals into pricing models, market participants can better capture the potential price range within which an NFT asset’s value may fluctuate, allowing for more accurate valuation assessments.

We aim to estimate confidence intervals for NFT asset volatility, providing a comprehensive framework for understanding and quantifying the uncertainty surrounding these unique digital assets.

Why is Interval Estimation More Effective Than Point Estimation?

NFTBank’s Valuation model aims to estimate the current asset value of NFTs using transaction data. Estimation can generally be divided into two types: point estimation and interval estimation. Point estimation involves estimating a single value, providing a concise and easily interpretable result.However, the limitation of point estimation lies in its inability to adequately reflect uncertainty based solely on the estimated value. To address this limitation, interval estimation is used to evaluate the reliability and uncertainty of the estimation more accurately.

Unlike point estimation, which aims to estimate a single point, interval estimation presents results as a range, acknowledging uncertainty and providing information about the possible values the estimated quantity can take with a certain level of confidence. This approach offers more statistical information by explicitly indicating the range of values that can be attributed to the estimated value.

Generally, interval estimation involves iterative estimation of estimation errors and establishing intervals based on assumptions about the distribution of the estimated value. However, such processes often require substantial computational resources, prompting us to explore alternative approaches for estimation. Therefore, based on these considerations, we intend to introduce quantile regression as a means to estimate intervals in our analysis.

How Did We Enable Interval Estimation?

To enable interval estimation, we employed the concept of quantile regression, which involves estimating quantiles of a distribution. Quantile regression provides a more robust estimation approach by directly estimating quantiles instead of relying solely on point estimates. This leads to more reliable and accurate interval estimations, considering the uncertainty and variability in the data.

It is known that the parameters and corresponding predictions that minimize the check loss represent the predictions for the tau-quantiles. Therefore, to obtain the desired confidence interval at a given significance level alpha, we constructed a model that simultaneously estimates the lower, medium, upper quantiles with respect to significance level alpha.

An intuitive example for our confidence interval

However, many non-linear models, including neural networks, face a critical issue in estimating multiple quantiles simultaneously, known as the crossing problem.

The crossing problem refers to the occurrence of inversions between the predicted values of two quantiles. This means that the 40% quantile may have a higher value than the 60% quantile, which violates the properties of quantiles. When inversions occur, the range of values for the predicted interval cannot be preserved, necessitating pre- or post-hoc adjustments.

An example for crossing problem. Some of those lower quantiles are cross over upper quantiles.

At NFTBank, we developed a model structure to address the crossing problem. Firstly, we created a custom objective function capable of estimating multiple quantiles, enabling us to utilize first-order optimization by computing the gradients. Additionally, we leveraged the monotonicity condition within the LightGBM module to ensure that the monotonicity condition holds for the estimated quantiles.

By implementing these methods, we successfully enabled interval estimation, allowing us to estimate quantiles and construct reliable confidence intervals for NFT asset valuation and volatility analysis.

Conclusion

For this article, we covered the importance of volatility in the NFT pricing ecosystem and how we manage the influence of volatility through our NFT Estimate Confidence Interval. Through a proper confidence interval, users can get a range of uncertainties compared to a single point to manage risk for different digital assets and optimize their portfolios.

The confidence interval is opened for free for a limited time only, before it goes to the Pro+ version. Test it out right now on our API Docs page.

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