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:

• GIA¹-certified diamonds
  • Round: 3EX² (cut, polish, symmetry), non-fluorecent
  • Cushion Modified Brilliant: depth 60–67%, excellent polish and symmetry, non-fluorecent
• 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 constraints³ (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 non-representative outliers, we select the second or third lowest price per carat for specific clarity grades (FL–VS1: second; VS2–SI2: third) based on market behavior, as the lowest per-carat prices may reflect atypical stones or listing errors. This method ensures competitive but stable retail asks, balancing accessibility and pricing integrity.

In cases where a required color–clarity combination has no available listing in the current observation window, the system applies a bounded historical lookup, querying past listings (up to five days prior) to find valid prices that meet selection rules. This approach, akin to last observation carried forward techniques used in financial indices such as BCOM, ensures continuity in matrix construction without introducing artificial smoothing or estimation. Only publicly listed prices are considered for core selection. In carat–grade regions where no valid listings exist over the observation window, the model uses structurally inferred prices derived from adjacent carat bands. These are computed via constrained extrapolation in log-space and applied only when consistent directional signals exist. Inferred entries serve to maintain matrix continuity, not to fill noise, and are excluded from behavioral calibration layers.

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:

• $i$: numeric color index (D=0, E=1, …, J=6)
• $j$: numeric clarity index (IF=0, VVS1=1, …, 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. For Cushion Modified Brilliant (CMB), we replace GIA cut grade with equivalent visual filters: 60–67% depth, EX polish/symmetry, no fluorescence.

Nonlinear Residual Adjustment

In cases with sufficient data density, we apply a second-stage correction using ALS⁴ (Alternating Least Squares). This fits a low-rank model to residuals between actual log-prices and the initial regression, capturing nonlinear effects omitted by the initial regression. This improves local fit without compromising model interpretability

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

Behavioral Adjustment Layer

Within a fixed carat band, carat-driven discontinuities disappear, but structured valuation biases persist in grade-based preferences. Two behavioral effects are applied to the reconstructed base matrix:

• Prospect aversion: sensitivity to perceived quality loss when deviating from the top-left (D/IF) combinations, modeled as exponential decay from the origin⁵
• Veblen premiums: small price uplifts for high-rank color/clarity pairs due to exclusivity signaling⁶

These adjustments are applied post-ALS reconstruction or to raw band matrices:

$$ P_{\text{adj}} = P_{\text{base}} \cdot \left[1 + \alpha e^{-\beta x} + \phi \left(1 - \frac{\text{rank}}{\text{max rank}} \right)^2 \right] $$

Where:

• $x$: Manhattan distance from (0, 0), approximating downgrade severity
• $\text{rank}$: row-major cell index, ranking rarity within the matrix
• $\alpha, \beta, \phi$: fixed hyperparameters calibrated to empirical price deviations

Anchoring effects are excluded here, as carat is constant within each matrix and addressed separately during cross-band interpolation⁷.

Cross-Carat Smoothing & Monotonic Enforcement

Once anchor matrices are constructed for each carat band (via log-linear regression and ALS), we apply a second-stage smoothing pass across carat values. This enhances consistency across adjacent bands and corrects for sampling noise or irregular listings that may cause per-carat price reversals.

We implement two sequential transformations:

Kernel Smoothing (Cross-Carat)

For each color–clarity cell $(i, j)$, we smooth prices across carat using a Gaussian-weighted average in log-space:

$$ \log P_c^{(i,j)} = \frac{\sum_k K(c, c_k) \cdot \log P_{c_k}^{(i,j)}}{\sum_k K(c, c_k)} \quad \text{with} \quad K(c, c_k) = \exp\left(-\frac{(c - c_k)^2}{2\sigma^2}\right) $$

Where:

• $c_k$: anchor carat bands (e.g., 0.30, 0.40, …, 6.00)
• $\sigma$: smoothing bandwidth, typically 0.10ct
• $P_{c_k}^{(i,j)}$: log-price estimate at carat $c_k$, color $i$, clarity $j$

This ensures smooth transitions across carat thresholds (e.g., 0.99 vs 1.00ct) and suppresses local anomalies.

Monotonic Regression (Per Cell)

After smoothing, we enforce carat-wise monotonicity per $(i,j)$ cell:

$$ \log P_{c_1}^{(i,j)} \leq \log P_{c_2}^{(i,j)} \leq \cdots $$

This is performed using isotonic regression via pool adjacent violators algorithm (PAVA). It guarantees a non-decreasing sequence of log-prices across carat.

Since a lighter diamond can be cut from a heavier one of identical grade, per-carat prices must not decrease with weight.

As a safeguard against rounding artifacts or kernel side effects, we apply a final strict clamping pass. If:

$$ \log P_{c_k}^{(i,j)} < \log P_{c_{k-1}}^{(i,j)} $$

we forcibly set $P_{c_k}^{(i,j)} := P_{c_{k-1}}^{(i,j)}$.

Price Interpolation Model

Price is modeled as a smooth, log-transformed function of carat, color, and clarity. To account for nonlinear carat scaling, we apply log-linear interpolation between band-specific price matrices. Each matrix is constructed at anchor carat weights (e.g., 0.30, 0.50, 0.70, 1.00, etc.).

Given a target carat $c \in [c_1, c_2]$, the base interpolated price is:

$$ P_c(i,j) = \exp\left((1 - \lambda) \cdot \log P_1(i,j) + \lambda \cdot \log P_2(i,j)\right), \quad \lambda = \frac{c - c_1}{c_2 - c_1} $$

• $P_1$, $P_2$: reference matrices at band endpoints $c_1, c_2$
• Interpolation is done per cell in log-space to preserve multiplicative scaling

To reflect buyer sensitivity around round-number weights (e.g., 0.99 ct vs. 1.00 ct), we apply a one-sided anchoring adjustment—boosting only when the carat is just below a psychological threshold:

$$ P_{\text{final}} = P_c \cdot \left[1 + \gamma e^{-\delta (t - c)} \right] \quad \text{if } c < t $$

• $t \in {0.3, 0.4, 0.5, 0.7, 0.9, 1.0, 1.5, 2.0, 3.0}$
• $\gamma \approx 0.1$, $\delta \approx 300$
• Active only within ~0.03 ct of $t$
• Capped to ≤80% of price delta to maintain monotonic scaling

This ensures price continuity and enforces monotonic carat scaling while capturing well-documented anchoring effects⁷.

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. DCX tracks only GIA-certified round brilliant diamonds with 3EX cut, no fluorescence. Fancy shapes are excluded due to lack of standardized cut grading and pricing variability.

Visualization Note: Specs 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 specs with large price variance.

Construction Methodology:

• Benchmark Basket: Spec count balances index stability with sensitivity to market shifts; updated quarterly.
• Weights: Assigned by estimated global volume × price turnover; rebalanced periodically.
• Pricing Source: Each spec refers to a unique combination of carat, color, and clarity (assumes GIA grading, 3EX, and non-fluorecent).

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 spec i at time t and $w_i$ is its weight.

This formulation computes a geometric mean of interpolated per-carat prices, weighted by spec 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

DCX draws exclusively from matrices built using publicly listed retail prices. No lab-grown or uncertified stones are included. DCX is recalculated daily and published with full spec-level transparency.

Real DCX (Monetary-Neutral Valuation)

The standard DCX reflects nominal USD pricing — the offer-side quotes for natural GIA-certified diamonds observed across major retail platforms. While this captures real market pricing, it does not isolate diamond value from movements in the dollar itself.

USD pricing can shift for reasons unrelated to the asset:

• Foreign exchange fluctuations — changes in USD strength relative to other currencies
• Inflationary drift — long-term erosion in the dollar’s purchasing power

To remove these distortions, we compute the Real DCX: a monetary-neutral version of the index that adjusts for both FX exposure and fiat degradation. It expresses diamond pricing in constant-value USD terms, enabling clearer long-term comparison. The latest Real DCX series follows:

Methodology

The Real DCX is calculated as:

$$ \text{Real DCX}_t = \frac{\text{DCX}_t}{\text{DXY}_t^{0.6} \cdot \text{XAU}_t^{0.4}} $$

Where:

• DXY reflects the trade-weighted strength of the USD across major fiat currencies
• XAU Gold approximates real-value erosion of the USD over time, serving as a non-fiat benchmark

Synthetic Anchor Construction

In charting, we include two synthetic anchor lines: DCX/USD [DXY] and DCX/USD [XAU]. These are not standalone indices, but scaled projections showing how the nominal DCX would evolve if driven solely by USD strength (via DXY) or by store-of-value effects (via gold), respectively.

Each anchor is calculated by re-scaling the nominal DCX using the relative movement of the benchmark asset from the base date:

DXY Anchor:

$$ \text{Anchor}_{\text{DXY},t} = \text{DCX}_0 \cdot \frac{\text{DXY}_t}{\text{DXY}_0} $$

Gold Anchor:

$$ \text{Anchor}_{\text{XAU},t} = \text{DCX}_0 \cdot \frac{\text{XAU}_t}{\text{XAU}_0} $$

Where $DCX_0$, $DXY_0$, and $XAU_0$ are values on the base reference date (typically the first date in the series $t=0$). This normalization allows for clean visual comparison on the same USD scale.

These anchors provide directional context — helping identify whether DCX price changes are more aligned with macro currency trends or diverging due to diamond-specific demand and supply conditions. They are not used in index computation and are shown for interpretive purposes only.

Weighting Rationale

• 60% DXY: Diamond pricing is sensitive to USD-driven capital flows, especially in FX-exposed consumer markets and cross-border retail channels.
• 40% Gold: While diamonds have partial store-of-value characteristics, they are not monetary reserves or inflation hedging instruments.

This composition reflects observed market behavior and can be revised if macro conditions or trading patterns evolve.

Interpretation Framework

Usage

The Real DCX is a non-quoted, analytical series displayed alongside the nominal DCX for interpretive purposes. It is not used for pricing, settlement, or trading. Its role is to:

• Normalize diamond price movements across monetary regimes
• Distinguish market-driven appreciation from currency effects
• Support macro-level evaluation of diamond pricing signals

Both the nominal and real indices are derived from the same OpenFacet pricing matrices and remain fully transparent and reproducible.