MantissaFi

Fully On-Chain European Options Protocol with Black-Scholes Pricing Engine

Architecture • Getting Started • Contracts • Math Engine • Testing • Security • Contributing

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Overview

MantissaFi is a fully on-chain European options protocol that computes Black-Scholes-Merton pricing, Greeks (Delta, Gamma, Theta, Vega), and the cumulative normal distribution function (Φ) entirely in Solidity — with provable accuracy bounds and gas efficiency.

Key Innovations

• Gas-Optimized BSM Engine — Full Black-Scholes pricing in <80K gas using PRBMath SD59x18 with Rational Chebyshev approximation for Φ(x) achieving <0.0001% error
• Liquidity-Sensitive IV Surface (LSIVS) — On-chain implied volatility derived from realized volatility, skew modeling, and pool utilization — no off-chain IV oracle dependency
• On-Chain Greeks — Delta, Gamma, Theta, Vega computed fully on-chain with shared intermediate values
• Formally Verified — Certora/Halmos invariant proofs for solvency, put-call parity, pricing monotonicity, and CDF bounds

How It Differs from Existing Protocols

Feature	Lyra/Derive	Dopex/Stryke	Panoptic	MantissaFi
Pricing model	BSM (off-chain IV)	BSM (off-chain IV)	Oracle-free (LP)	BSM (fully on-chain)
IV source	GWAV + Deribit	External	N/A	On-chain LSIVS
Greeks on-chain	❌	❌	Partial	✅ Full suite
Formal verification	❌	❌	❌	✅ Certora proofs
Gas per price	N/A (off-chain)	N/A (off-chain)	~80K	< 80K

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Architecture

┌─────────────────────────────────────────────────────────────────┐
│                       MantissaFi Protocol                       │
├─────────────────────────────────────────────────────────────────┤
│                                                                 │
│  ┌──────────────┐  ┌──────────────┐  ┌───────────────────────┐ │
│  │  OptionVault  │  │  BSMEngine   │  │  VolatilitySurface    │ │
│  │              │  │              │  │                       │ │
│  │ • mint()     │──│ • price()    │──│ • getIV()             │ │
│  │ • exercise() │  │ • delta()    │  │ • updateRealizedVol() │ │
│  │ • settle()   │  │ • gamma()    │  │ • skewAdjust()        │ │
│  │ • liquidate()│  │ • theta()    │  │ • utilizationAdjust() │ │
│  └──────┬───────┘  │ • vega()     │  └───────────┬───────────┘ │
│         │          │ • cdf()      │              │             │
│         │          └──────────────┘              │             │
│  ┌──────▼───────┐  ┌──────────────┐  ┌──────────▼────────────┐ │
│  │ LiquidityPool│  │  FixedPoint  │  │  OracleAdapter        │ │
│  │              │  │  MathLib     │  │                       │ │
│  │ • deposit()  │  │ • exp()      │  │ • Chainlink            │ │
│  │ • withdraw() │  │ • ln()       │  │ • Pyth                │ │
│  │ • allocate() │  │ • sqrt()     │  │ • TWAP                │ │
│  │ • hedgeDelta │  │ • cdf()      │  │ • RealizedVol         │ │
│  └──────────────┘  │ • pdf()      │  └───────────────────────┘ │
│                    └──────────────┘                             │
│  ┌──────────────┐  ┌──────────────┐  ┌───────────────────────┐ │
│  │ OptionToken  │  │  Settlement  │  │  AccessControl        │ │
│  │  (ERC-1155)  │  │   Engine     │  │  & Governance         │ │
│  └──────────────┘  └──────────────┘  └───────────────────────┘ │
└─────────────────────────────────────────────────────────────────┘

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Getting Started

Prerequisites

• Foundry (forge, cast, anvil)
• Node.js >= 18 (for tooling)
• Python >= 3.10 (for differential testing)

Installation

git clone https://github.com/0xfandom/mantissa-fi.git
cd mantissa-fi
forge install

Build

forge build

Test

# Unit tests
forge test

# Fuzz tests (10,000 runs)
forge test --match-path "test/fuzz/*" -vvv

# Gas report
forge test --gas-report

# Fork tests (requires RPC URL)
FORK_URL=<your-rpc-url> forge test --match-path "test/fork/*" --fork-url $FORK_URL

Deploy (Testnet)

forge script script/Deploy.s.sol --rpc-url $RPC_URL --broadcast --verify

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Contracts

src/
├── core/
│   ├── OptionVault.sol              # Main entry — mint, exercise, settle options
│   ├── LiquidityPool.sol            # LP deposits, withdrawals, delta hedging
│   ├── OptionToken.sol              # ERC-1155 multi-token for option positions
│   └── Settlement.sol               # Expiry settlement, ITM/OTM resolution
├── pricing/
│   ├── BSMEngine.sol                # Black-Scholes-Merton pricing engine
│   ├── FixedPointMathLib.sol        # exp, ln, sqrt optimized for BSM
│   ├── CumulativeNormal.sol         # High-precision Φ(x) — Hart's approximation
│   └── Greeks.sol                   # Delta, Gamma, Theta, Vega computation
├── volatility/
│   ├── VolatilitySurface.sol        # LSIVS — implied volatility surface
│   ├── RealizedVolOracle.sol        # EWMA realized volatility from price feeds
│   └── SkewModel.sol                # Strike-dependent IV adjustment
├── oracle/
│   ├── OracleAdapter.sol            # Multi-oracle: Chainlink + Pyth + TWAP
│   └── PriceValidator.sol           # Staleness & deviation checks
├── periphery/
│   ├── OptionRouter.sol             # User-facing multicall helper
│   ├── OptionLens.sol               # View functions for frontends
│   └── FeeController.sol            # Dynamic fee model
└── libraries/
    ├── OptionMath.sol               # Payoff calculations, moneyness helpers
    ├── TimeLib.sol                  # Timestamp → annualized time conversion
    └── Constants.sol                # Fixed-point constants (√2π, e, etc.)

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Math Engine

Black-Scholes Formula

C = S · Φ(d₁) - K · e^(-rT) · Φ(d₂)

d₁ = [ln(S/K) + (r + σ²/2) · T] / (σ · √T)
d₂ = d₁ - σ · √T

On-Chain CDF: Hart's Rational Approximation

The cumulative normal distribution Φ(x) is computed using a 7-term rational polynomial achieving < 7.5 × 10⁻⁸ maximum error at approximately 8,000 gas.

Gas Targets

Operation	Target Gas
Φ(x) — CDF	< 10,000
Full BSM price	< 80,000
All 4 Greeks	< 100,000
Mint option	< 150,000
Exercise option	< 100,000

Precision Guarantees

All pricing outputs are validated against scipy.stats.norm (Python) across 10,000+ fuzzed input vectors:

• CDF max error: < 1 × 10⁻⁵
• BSM price max relative error: < 0.01%
• Put-call parity deviation: < 0.001 USDC per option

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Testing

Test Categories

Category	Location	Description
Unit	test/unit/	Individual function correctness
Fuzz	test/fuzz/	Property-based with random inputs
Invariant	test/invariant/	Protocol-wide invariant testing
Integration	test/integration/	Full option lifecycle
Fork	test/fork/	Against mainnet state
Differential	test/differential/	Solidity vs Python reference
Gas	test/gas/	Gas benchmarking suite

Running Differential Tests

cd analysis/
pip install -r requirements.txt
python precision_test.py  # Generates test vectors
cd ..
forge test --match-path "test/differential/*"

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Security

Formal Verification (Certora / Halmos)

Invariant	Description	Status
Solvency	Pool assets ≥ max payoff obligations	🔲
Pricing Monotonicity	∂C/∂S > 0, ∂P/∂S < 0, Vega > 0	🔲
Put-Call Parity	C - P = S - K·e^(-rT) within ε	🔲
CDF Bounds	0 ≤ Φ(x) ≤ 1, Φ(-x) = 1 - Φ(x)	🔲
No Value Extraction	profit ≤ intrinsic - premium	🔲

Static Analysis

slither src/
aderyn .

Threat Model

See SECURITY.md for the complete threat model covering oracle manipulation, flash loan attacks, precision exploits, IV manipulation, and donation attacks.

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Project Roadmap

• Phase 0: Project setup, repository structure
• Phase 1: Math engine (CDF, BSM, Greeks) — Weeks 1–3
• Phase 2: Protocol core (Vault, Pool, Settlement) — Weeks 4–7
• Phase 3: Volatility surface (LSIVS, EWMA, Skew) — Weeks 8–10
• Phase 4: Security & formal verification — Weeks 11–13
• Phase 5: Documentation, paper, presentation — Weeks 14–16

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Tech Stack

Component	Technology
Language	Solidity ^0.8.25
Framework	Foundry
Math Library	PRBMath v4 (SD59x18)
Token Standard	ERC-1155 (OpenZeppelin)
Oracle	Chainlink, Pyth, Custom TWAP
Formal Verification	Certora / Halmos
Static Analysis	Slither, Aderyn
Differential Testing	Python (scipy, numpy)

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Contributing

Contributions are welcome! Please read CONTRIBUTING.md before submitting PRs.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Run tests (forge test)
4. Commit changes (git commit -m 'feat: add amazing feature')
5. Push to branch (git push origin feature/amazing-feature)
6. Open a Pull Request

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License

This project is licensed under the MIT License — see the LICENSE file for details.

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Acknowledgements

• PRBMath — Fixed-point arithmetic
• SolStat — Statistical functions in Solidity
• OpenZeppelin — Security standards
• Black, F. & Scholes, M. (1973) — The Pricing of Options and Corporate Liabilities
• Abramowitz & Stegun (1964) — Handbook of Mathematical Functions