Methodology Overview

This section documents the mathematical foundations of Funding Yield OS. The system is designed to be deterministic, auditable, and reproducible.

Design Principles

Pessimistic by default — Assume funding will decay, not persist
Explicit assumptions — All defaults are stated, not hidden
Deterministic computation — Same inputs produce same outputs
Reproducible results — Metrics can be reconstructed from raw data

Core Model Pipeline

Raw Funding Data
     ↓
Funding Rate Model (Annualization)
     ↓
Persistence Model (Half-Life, Decay)
     ↓
Survivability Model (Mirage Adjustment)
     ↓
Capacity Model (Crowding Effects)
     ↓
Simulation Engine (Position-Level PnL)
     ↓
Trust Layer (Reliability Grading)

Notation Reference

Symbol	Meaning
$f$	Funding rate per interval
$\Delta t$	Funding interval in hours (typically 8)
$N_y$	Funding intervals per year (typically 1095)
$APR_f$	Annualized funding APR
$\lambda$	Exponential decay coefficient
$t_{half}$	Funding half-life in hours
$h$	Holding horizon in hours
$D$	Decay factor
$S$	Survivability factor
$APR_{surv}$	Survivable APR
$M$	Mirage ratio
$C_{soft}$	Soft capacity (USD)
$C_{hard}$	Hard capacity (USD)
$P_{cap}$	Capacity penalty factor
$OI$	Open interest (USD)

Conventions

APR values are expressed in percent points (e.g., 50.0 = 50%)
Ratios are stored in [0, 1] space
Capacity values are in USD
Scores are on [0, 100] scale
Money values round to cents only at presentation boundaries

Documentation Sections

Funding Rate Model — Annualization and raw rate handling
Persistence & Decay — Half-life estimation and decay modeling
Survivability Model — Mirage ratio and survivable APR
Capacity Model — Crowding effects and capacity curves
Simulation Engine — Position-level PnL calculation
Trust Layer — Reliability grading and prediction accuracy

Source Reference

This documentation is derived from the internal Mathematical Specification, which serves as the canonical reference for engineering, QA, and audit purposes.

Capital Planner Funding Rate Model