About OpenFacet & DCX Methodology

OpenFacet is a transparent framework for constructing smooth, explainable diamond price matrices using observable market data. It relies on log-linear regression over structured carat–color–clarity tuples, capturing pricing gradients while excluding irrelevant or unreliable data.

Key principles:

GIA-certified, fluorescence-free round diamonds only
Model granularity per industry standard carat bands (e.g., 0.30–0.39ct)
Interpolated prices via log-space smoothing across carat bands
Competitive pricing floor via lowest observable public retail ask
Reconstructed matrices follow monotonicity constraints (better grades should not be priced lower)

The DCX Composite provides a benchmark for retail diamond pricing, algorithmic strategies, synthetic asset valuation, and quantitative market analysis.

Data Sources

Prices are collected from inventories provided by top-tier online retailers. Sources must:

Publish retail-grade SKUs with full GIA details (cut, color, clarity, carat, cert ID)
Provide live or frequently updated pricing

We exclude suppliers with inconsistent pricing, aggressive caching, or non-GIA certification standards.

Price Selection Logic

To avoid misrepresentative outliers often present in public listings—especially in thin or high-variance clarity segments—we select near-floor prices based on clarity-tier behavior. In higher clarities (FL to VS1), extreme low prices typically reflect atypical stones or listing artifacts. In mid-tier clarities (VS2 to SI2), broader price dispersion makes the lowest few prices unreliable for index construction. Our method selects competitive but stable retail asks, balancing accessibility with pricing integrity.

Price Matrix Reconstruction

For each carat band, we reconstruct a complete color × clarity price matrix using a log-linear regression model. Retail listings are incomplete—many color/clarity combinations have no recent asks, especially in lower-demand segments.

We assume that within a fixed carat band, diamond log-price $\log(p)$ varies smoothly with color and clarity. Each known sample is encoded as:

$i$: color index (e.g., D=0, J=6)
$j$: clarity index (e.g., IF=0, SI2=6)
$y = \log(p)$: log-transformed ask price

We fit a model of the form:

$$ \log(p_{i,j}) = \beta_0 + \beta_1 \cdot (i - \bar{i}) + \beta_2 \cdot (q_j - \bar{q}) $$

Where:

$\bar{i}, \bar{q}$: centered indices (color, reversed clarity)
$q_j$: clarity quality score (IF → high → large $q$)
$\beta_0, \beta_1, \beta_2$: regression coefficients via least squares

We restrict to GIA Excellent cut to isolate the effects of color and clarity.

After fitting, we reconstruct the full matrix by evaluating the regression on all grid points, exponentiating to recover prices, and enforcing monotonicity:

Price should not increase when moving to lower color or clarity grades

Nonlinear Residual Adjustment

In cases with sufficient data density, we apply a second-stage correction using ALS (Alternating Least Squares). This fits a low-rank model to residuals between actual log-prices and the initial regression, capturing nonlinear interactions not captured by the initial regression. This enhances local accuracy while preserving interpretability.

This hybrid approach produces stable, smooth, and data-aligned price surfaces suitable for display, index computation, or further modeling.

Price Interpolation Model

Diamond prices are modeled as a smooth function over carat, color, and clarity. Due to the nonlinear nature of diamond pricing—especially with respect to carat weight—our system uses log-linear interpolation in price space rather than simple linear averaging.

We precompute standardized price matrices across multiple carat bands (e.g., 0.30–0.39 ct, 0.40–0.49 ct, …, 2.0–2.99 ct), each structured as a matrix over color (D–J) and clarity (IF–SI2).

To interpolate a matrix at any intermediate carat value $c$ within a band $[c_1, c_2]$, we apply geometric interpolation between two anchor matrices $P_1$ and $P_2$:

$$ P_c(i,j) = \exp\left((1 - \lambda) \cdot \log P_1(i,j) + \lambda \cdot \log P_2(i,j)\right) $$

where:

$P_c(i,j)$: interpolated price at carat $c$, color $i$, clarity $j$
$P_1, P_2$ are the reference price matrices at $c_1, c_2$
$\lambda = \frac{c - c_1}{c_2 - c_1}$
$i, j$ index over color and clarity
All interpolation is done in log-space to reflect multiplicative scaling in market behavior

This method ensures pricing reflects real-world supply constraints: doubling carat typically increases per-carat price, not just total price.

Interpolated matrices are used for visual display, analytical modeling, and index construction (e.g., Diamond Composite Index). Only smoothed, log-transformed outputs based on public retail data are published.

DCX: Diamond Composite Index

DCX is a synthetic price index derived from OpenFacet matrices, designed to track retail-level diamond price trends for benchmarking and financial use.

Visualization Note: SKU contributions shown in visual displays (e.g., bar charts) are based on raw weighted dollar value: carat × per-carat price × weight, scaled relative to the largest contributor. This differs from the DCX calculation, which uses smoothed, interpolated per-carat prices and normalized weights.

Index Rationale: Unlike commodity indices (e.g., BCOM), which use arithmetic means over exchange-traded futures, DCX follows a geometric mean construction similar to Jevons-style consumer price indices. This reflects the multiplicative nature of diamond pricing, where increases in quality or carat weight compound rather than add. The log–exp formulation also mitigates outlier sensitivity and ensures smoother, scale-consistent behavior across SKUs with large price variance.

Construction Methodology:

SKU Basket: SKU count balances index stability with sensitivity to market shifts; updated quarterly.
Weights: Assigned by estimated global volume × price turnover; rebalanced periodically.
Pricing Source: Each SKU is priced using its interpolated per-carat value from the OpenFacet model.

The index is computed as a weighted geometric mean of per-carat prices:

$$ DCX_t = \exp\left( \frac{\sum w_i \cdot \log P_{i,t}}{\sum w_i} \right) $$

where $P_{i,t}$ is the estimated per-carat price of SKU i at time t and $w_i$ is its weight.

This formulation computes a geometric mean of interpolated per-carat prices, weighted by SKU turnover. The geometric mean reduces the influence of outliers and aligns with the multiplicative behavior of diamond pricing across grades and sizes.

This construction ensures:

Resistance to outliers (log-mean smooths spikes)
Representativeness across carat, color, clarity ranges
Interpretability for financial or synthetic asset settlement use cases