dbis_core/docs/volume-iii/pricing-models.md

GRU Bond Pricing Models

Overview

GRU bond pricing models provide comprehensive valuation frameworks accounting for perpetual bond structures, index adjustments, and multi-reality settlement considerations.

Base Pricing Model

Formula

Price = PV(Coupons) + PV(Perpetual Component) + Index Adjustment(LiXAU/LiPMG/etc.)

Components

Present Value of Coupons

PV(Coupons) = Σ(Coupon[i] / (1 + r)^t[i])

Where:

• Coupon[i] = Coupon payment at period i
• r = Discount rate
• t[i] = Time to coupon payment i

Present Value of Perpetual Component

PV(Perpetual) = Principal / r

For perpetual bonds, the principal value is discounted at the required rate of return.

Index Adjustment

Index Adjustment = Principal × (IndexValue / BaseIndexValue - 1) × IndexWeight

Where:

• IndexValue = Current index value (LiXAU, LiPMG, etc.)
• BaseIndexValue = Index value at bond issuance
• IndexWeight = Weight of index in bond pricing

Discounted Acquisition Model

Formula

Acquisition Price = Nominal / 0.15

Purpose

Used for reserve expansion and sovereign acquisition of GRU bonds.

Characteristics

• High discount (85% off nominal)
• Reserve expansion mechanism
• Sovereign access pricing
• Long-term holding incentive

GRU Liquidity Loop-Linked Yield

Formula

Yield = f(7→10→9.55 cycles, Index Volatility, Sovereign Risk)

Components

Liquidity Loop Cycles

The 7→10→9.55 cycle represents:

• Initial capital: 7 GRU
• Quantum mint: 10 GRU
• FX/spread deduction: 9.55 GRU
• Reinjection into next cycle

Index Volatility

Index Volatility = σ(IndexReturns) × VolatilityWeight

Sovereign Risk

Sovereign Risk = SRI_Score × RiskWeight

Yield Calculation

Yield = BaseYield + LoopAdjustment + VolatilityAdjustment - RiskPenalty

Where:

• BaseYield = Base GRU bond yield
• LoopAdjustment = f(cycle efficiency, loop iterations)
• VolatilityAdjustment = Index volatility impact
• RiskPenalty = Sovereign risk premium

Index-Linked Pricing

LiXAU (Gold Index)

Price Adjustment = Principal × (XAU_Price / XAU_Base) × XAU_Weight

LiPMG (PGM Basket Index)

Price Adjustment = Principal × (PGM_Index / PGM_Base) × PGM_Weight

LiBMG (BMG Basket Indices)

Price Adjustment = Principal × Σ(BMG[i]_Weight × (BMG[i]_Price / BMG[i]_Base))

Perpetual Bond Specific Pricing

Perpetual Component Valuation

For 99-year perpetual bonds:

Perpetual Value = Annual Coupon / Required Yield

Buy-Back Option Pricing

For 10-year buy-back option:

Option Value = PV(Principal at Buy-Back) - PV(Coupons Lost)

Multi-Reality Pricing

Quantum State Pricing

Price_Quantum = Σ(Probability[i] × Price[i])

Parallel Reality Pricing

Price_Parallel = Average(Price[Reality[i]])

Holographic Pricing

Price_Holographic = Project(Price_Classical, Holographic_Field)

Merged Pricing

Price_Merged = Merge(Price_Classical, Price_Quantum, Price_Parallel, Price_Holographic)

Pricing Service Integration

Real-Time Pricing

• Continuous price updates
• Index value feeds
• Market data integration
• Automated recalculation

Historical Pricing

• Price history tracking
• Performance analytics
• Volatility calculations
• Risk metrics

Pricing Validation

• Model validation
• Backtesting
• Stress testing
• Regulatory reporting