Original author: Yusen Zhan, Black, Ziang (Tony) Ling

Original compilation: Deep Chao TechFlow

Note: This article comes from Stanford Blockchain Review. TechFlow is a partner of Stanford Blockchain Review and is exclusively authorized to compile and reprint.

introduce

In the evolving world of non-fungible tokens (NFTs), effective pricing models require a balance between complexity and explainability. For example, the floor price indicator is often used in NFT transactions. In many cases, although the floor price reflects a rough starting point and baseline indicators, it usually does not accurately reflect the intrinsic value or characteristics of the NFT.

Historically, many NFT pricing models have relied on gradient boosted decision trees (GBDT). Although they provide reliable predictions, they are complex and difficult to interpret. In this article, we introduce a new premium valuation model that aims to create a new valuation model that takes into account market infrastructure and fundamental principles. We hope that by capturing more of the nuanced characteristics of NFTs, creators, traders, and collectors in the NFT space can better understand the complexity of NFT pricing.

Baseline: Gradient-based decision tree model

Currently, a common modeling technique for NFT pricing is the gradient boosted decision tree, or GBDT. This ensemble learning approach originates from the basic principles of decision trees, where a single tree makes decisions based on set criteria. However, GBDT is unique in that it builds multiple trees consecutively. Each time a new tree is built, it attempts to correct the errors of the previous tree and gradually improve the accuracy of the integration. This systematic, iterative approach gives GBDT models the ability to identify and integrate complex data patterns and subtle differences.

Advantages of the GBDT model

• Resilience: GBDT is able to withstand outliers in the data set, making it suitable for a variety of data scenarios.

• Handle mixed data: GBDT can seamlessly manage datasets containing both categorical and numeric features.

• Automatic feature selection: The nature of the model enables it to prioritize relevant features, often reducing the need for significant feature engineering.

• Reduced overfitting: Due to the nature of the ensemble and iterative correction, GBDT generally exhibits less overfitting than a single decision tree.

Challenges and limitations of the GBDT model

• Complexity: As an ensemble of multiple decision trees, understanding the inner workings of a GBDT or tracing a specific decision path can be complex.

• Training time: Due to its iterative nature, GBDT generally requires longer training time than simple models.

• Memory intensive: Storing multiple decision trees requires a large amount of memory, which can be a limitation in resource-limited environments.

Complexity and lack of transparency: core issues

In the context of our NFT pricing, the biggest challenge with GBDT is the lack of transparency. While the model may provide a price or valuation, it is a black box algorithm and cannot simply explain why a given price is arrived at.

One of the main advantages of GBDT, namely capturing subtle data patterns across multiple decision trees, becomes a double-edged sword when we need to justify or explain a pricing decision to stakeholders. This lack of clear interpretability makes pricing metrics difficult to understand for various stakeholders in the NFT space. Therefore, this emphasizes the importance of providing a pricing model that is both accurate and interpretable.

Premium Model Overview

As mentioned above, we are launching a premium model for NFT pricing that balances accuracy and explainability by aligning prices with the underlying principles and characteristics of these digital assets.

NFT pricing includes a collection-based value and a premium for its properties. The core formula of the premium model is as follows:

• Valuation: The predicted value of an NFT.

• Floor Price: The lowest selling price currently listed for an NFT in a specific collection or category on the market.

• Intercept: Can be viewed as a base adjustment to the floor price, taking into account inherent factors that may generally adjust upward or downward.

• Feature weight: The coefficient assigned to each feature to determine how that feature affects the price of the NFT. Each feature affects the estimated price in proportion to its relative value to the floor price.

• Feature Premium: The additional value assigned to an NFT’s specific, attractive features or characteristics. They are the product of the floor price and the corresponding feature weight.

• Collection-based value: This represents the baseline value of the NFT in the collection, derived from the floor price and may be affected by an intercept that takes into account general market conditions or other factors not related to the specific characteristics.

Derivation of premium valuation model

In the premium model, we use linear regression to analyze how specific characteristics affect the estimated price of an NFT. Using feature weights and floor prices as variables, the linear regression model can effectively predict the price of NFTs based on their inherent characteristics and current market baseline.

Under our premium model we have:

After simple transformation, we get:

Renaming the left side to y and the right side to linear regression form, we get:

in:

• y is the predicted output.

• x is a one-bit valid encoding vector representing the NFT characteristics. Each position in the vector represents a specific feature, and the vector at the position corresponding to the feature NFT has is"hot"(i.e., set to 1), otherwise zero.

• w is a weight vector, where each element represents the weight associated with a specific feature when determining the NFT price.

• b is the intercept, adjusting the prediction independently of the characteristics.

The wT * x term is calculated as the dot product of two vectors, that is:

In practical use, suppose you have 3 features (A, B, C). An NFT with properties B and C will be represented by a one-bit valid vector x = [0, 1, 1]. The linear regression model predicts the price of NFTs based on the weights and intercepts learned for each feature, so we can rewrite the sum of feature weights as wTx. We can use an open source machine learning library to implement a linear regression model and build our premium model based on the above analysis.

Assessment Demonstration

We can price the rare Bored Ape Yacht Club #7403 using our advanced pricing model. Below is the basic information corresponding to this token:

This NFT has various features including Trippy Fur, Faux Hawk Hat, Angry Eyes, Aquamarine Background, Silver Hoop Earring, and Phoneme Mouth. Of these, Trippy Fur is considered the rarest attribute. According to our GoPricing API, #7403s evaluation results are as follows:

"pricing"is the estimated price of token 7403, which is 104.42672366856866 ETH,"floor"It is the floor price at the time of request. Our estimated price can be broken down into:

From the above example, we just need to calculate the premium instead of the weight and display the final estimate to the user, as shown in the following demo:

Advantages of premium valuation models

Given the theoretical derivation and practical demonstration of the above valuation model, we can see how it provides a practical and market-consistent framework for pricing strategies. This in turn allows for a pragmatic, adaptive and transparent approach to valuation. We can summarize some of the main features and advantages of advanced assessment models as follows:

• Linear: The premium model maintains a linear relationship with the floor price, maintaining a consistent price ratio between NFTs and features based on a determined set of weights.

• Transparency: A standout feature is the inherent transparency of the model, as the parameters are not only easily verified but also provide clear visibility during the valuation process.

• Real-time responsiveness: The model is real-time, where the price of NFT reflects changes in the floor price, ensuring that valuations are always in sync with current market dynamics.

• Reliable neutrality: Avoiding third-party biases such as perceived rarity or sentimental value, parameters are derived via linear averages and are strictly based on transaction history, using only sales prices and floor prices as input during training.

• Interpretability:

• Clear parameters: Whether it is weight or intercept, each parameter has practical significance, clarifying the importance and basic value of the characteristics in the NFT field.

• Shared feature weights: Similar to how features are permeated across different NFTs, feature weights are shared across various NFT prices, ensuring a unified and consistent valuation approach.

The premium model therefore balances simplicity and complexity while ensuring transparency. By focusing on clarity, adaptability, and fairness, it provides a solid foundation for accurately and efficiently valuing NFTs.

in conclusion

Pricing models are crucial in the rapidly evolving NFT market, where transparency is highly valued. Although tree-based models such as GBDT have been popular, their complexity can pose challenges. To solve this problem, people turned to more transparent linear premium models.

Going forward, we expect to integrate premium models with NFT pricing oracles, lending protocols, and automated market makers (AMMs). For example, in NFT pricing oracles like Chainlink, premium models can refine pricing inputs and ensure more stable pricing feedback. In NFT lending protocols like BendDAO, advanced pricing models can facilitate secure NFT mortgage lending, opening up new avenues for NFT in DeFi.

Additionally, in NFT AMMs like Uniswap v4, advanced pricing models can enhance the conversion algorithm to align rewards with NFT value and rarity. Beyond this, the premium model can guide the decentralized ownership of NFTs, shape NFT indices, and drive the evolution of synthetic NFTs, while maintaining a strong, transparent, and user-friendly pricing mechanism in NFT platforms and financial applications.