Duration Model (Demand Side)

Last Updated: 2026-01-28

Liability Duration Analysis (Demand Side)

Purpose

Determine how much of the USDS liability base is short-term (could demand liquidity soon) versus long-term (sticky, unlikely to redeem).

Method: Lindy Duration Model

For each lot of USDS:

1. Measure current age (time since last transfer)
2. Expected remaining holding time = current age × Lindy factor
3. Apply conservative haircut (e.g., 0.5x or 0.7x instead of 1x pure Lindy)

Duration Bucket Structure

The Duration Bucket system uses a two-layer capacity calculation:

1. Daily Lindy Measurement — Dynamic calculation of liability duration distribution
2. Structural Maximum Caps — Governance-set upper limits per bucket, derived from empirical bank run research

Bucket Definitions

The system uses 101 buckets, each representing 15 days:

Bucket semantics:

• Liability side: Bucket N contains liabilities with expected remaining duration ≥ N × 15 days
• Asset side: Bucket N is required for assets with SPTP (Stressed Pull-to-Par) in the range [(N-1) × 15, N × 15) days
• Bucket 100: Captures all liabilities with expected duration ≥ 1,500 days (the structural/permanent base)

Structural Maximum Caps: Double Exponential Model

The structural caps follow a double exponential decay model calibrated to empirical bank run data:

Individual Cap(t) = A × e^(-λ₁ × t) + B × e^(-λ₂ × t)

Research-Calibrated Parameters:

Empirical Calibration Basis:

The parameters were fitted to match the aggressive end of empirical bank run research:

Key Research Sources:

• Basel III LCR/NSFR frameworks
• March 2023 bank runs: SVB, Signature Bank, First Republic, Credit Suisse
• MMF crisis data: September 2008 (26% in 2 weeks), March 2020 (30% in 2 weeks)
• ECB/Fed deposit behavior studies

Full Bucket Table

Reading the table:

• Individual: Maximum % of portfolio that can be in this specific bucket alone
• Cumulative: Maximum % of portfolio that can be in this bucket OR higher (used for asset matching)
• Bucket 100: The 9.52% cumulative includes the tail beyond 1,500 days — the structural/permanent holder base

Key Checkpoints

Note: These caps represent maximum allowable allocation even if Lindy measurement suggests higher capacity. Governance may adjust parameters based on observed USDS holder behavior.

Two-Layer Capacity Calculation

Layer 1: Daily Lindy Measurement Every day, measure USDS lot ages and calculate expected remaining duration to produce a "raw" liability distribution.

Layer 2: Apply Structural Caps For each bucket from longest to shortest:

Raw Capacity = Lindy-measured liability amount for this bucket
Cap = Max Cap % × Total Portfolio

If Raw Capacity > Cap:
  Effective Capacity = Cap
  Overflow = Raw Capacity - Cap
  → Overflow trickles down to next-lower bucket
Else:
  Effective Capacity = Raw Capacity

Example:

• Total portfolio: $10B
• Lindy says bucket 48 (720 days) has $500M (5% of portfolio)
• Bucket 48 cap is 2% = $200M
• Result: Bucket 48 gets $200M, remaining $300M trickles to bucket 45 (675 days)
• If bucket 45 also exceeds its cap after adding overflow, it trickles further down

Conservative Rounding Rules

Cumulative Capacity for Matching

An asset can match against its required bucket AND all higher buckets. Higher-tier capacity can always fulfill lower-tier requirements.

Example:

• An asset with 360-day SPTP requires bucket 24
• Available capacity = bucket 24 + bucket 30 + bucket 36 + ... + bucket 48 (cumulative)
• A 720-day liability can match a 360-day asset (but not vice versa)

Cumulative Capacity at Bucket N = Σ (Effective Capacity for all buckets ≥ N)

Duration Capacity Reservation System

Note: The tug-of-war mechanism and duration auctions described in this section are Phase 9+ features. Prior phases use manual, governance-directed duration matching allocations — see accounting/tugofwar.md for the algorithm details and phase dependencies.

Duration Bucket capacity is allocated to Primes through a reservation system. Primes acquire reservations via daily auctions, then can resell them on a secondary market.

Core Principles

1. Own-bucket priority is emergent — Primes tug at their own bucket with distance 0 (no decay), giving them natural priority without a separate allocation phase (see ../accounting/tugofwar.md)
2. All capacity allocated via tug-of-war — When Lindy doesn't match reservations, the tug-of-war mechanism redistributes capacity to Primes with unmet need
3. Full secondary market flexibility — Time-sliced ownership, partial amounts, arbitrary durations

Daily Cycle

Primary Auction

Auctions occur when unreserved capacity exists at a bucket. Primes bid price-per-epoch for capacity amounts. Highest bidders win. Winners receive reservations starting next epoch.

Secondary Market

Reservation holders can sell portions of their ownership with time-sliced schedules. Buyers can immediately resell, enabling complex ownership structures.

Capacity Allocation

All capacity is allocated through tugging — there's no special "own bucket first" phase. Primes tug at their own bucket with distance 0 (no decay), giving them natural priority there. But if their bucket is empty and a neighbor is full, they can still effectively tug nearby buckets.

Phase 1: Tug-of-War

All Primes tug for capacity simultaneously:

• Distance 0 (own bucket) = full tug strength, maximum effective value
• Distance N = tug decays by 0.9^N (floor at 10%)
• Tugging UP = effective value 1.0
• Tugging DOWN = effective value = target/your bucket
• Collisions resolved pro-rata
• Multiple rounds until all needs met or capacity exhausted

Phase 2: Trading

After needs are met, Primes can trade up:

• Tug at higher buckets with remaining excess
• Release lowest-value capacity downward
• Cascade until capacity finds a Prime that values it

See accounting/tugofwar.md for full algorithm details.

Capacity Duration Rules