Acastus: Risk Engine for Delta-Neutral Strategies

Risk modeling framework for delta-neutral strategies and stablecoin economics.

Theory

Delta-Neutral Portfolio Construction

A delta-neutral portfolio maintains zero first-order sensitivity to price movements:

• Long spot: Δ_spot = +Q
• Short derivative: Δ_derivative = -Q
• Net delta: Δ_portfolio = 0

Key Properties: Price independence for small moves, carry exposure via funding/basis, liquidation convexity introduces hidden gamma.

Greeks for Delta-Neutral Strategies

Delta (Δ): ∂V/∂S

• Target: Δ_portfolio ≈ 0 via continuous rebalancing
• Example: Long 10 ETH spot (Δ=+10) + Short 10 ETH perp (Δ=-10) = Net Δ=0

Gamma (Γ): ∂²V/∂S²

• Linear instruments have Γ ≈ 0, but liquidation mechanics create effective gamma near margin thresholds

Vega (ν): ∂V/∂σ

• Direct vega ≈ 0 (no options), but volatility affects funding rates, basis, and liquidity costs

Theta (Θ): ∂V/∂t

Total_Θ = Funding_Θ + Basis_Θ - Transaction_Cost_Θ

Time decay from funding payments and rebalancing costs.

Rho (ρ): ∂V/∂r

Funding rate sensitivity dominates delta-neutral P&L:

Funding_ρ = Position_Size × Mark_Price × Time_to_Funding

Basis Delta: ∂V/∂(Perp - Spot)

Primary risk when price delta is neutralized; basis changes create P&L even with perfect hedge.

Lambda (λ): ∂V/∂(Spread)

Liquidity sensitivity from rebalancing costs; stressed markets widen spreads when rehedging needed most.

Key Insights

1. Risk Shifts: From directional to basis, funding, and liquidity risks
2. Hidden Gamma: Liquidation mechanics create convexity with linear instruments
3. Funding Dominance: Rho often drives P&L in delta-neutral strategies
4. Correlation Risk: Spot-perp correlation breakdown breaks neutrality
5. Regime Sensitivity: Greeks change dramatically across market regimes

Perpetual Swap Mechanics

Funding Rate: Periodic payment anchoring perpetual to spot

Funding_Payment = Position_Size × Mark_Price × Rate × dt

• Positive: Longs pay shorts (perp at premium)
• Negative: Shorts pay longs (perp at discount)

Basis Risk: Basis = Perp_Price - Spot_Price
Driven by funding expectations, liquidity differences, and exchange-specific factors.

Risk Metrics

VaR: VaR_α = -Quantile(Returns, α) - Maximum expected loss at confidence level
ES: ES_α = -E[Returns | Returns < -VaR] - Average loss beyond VaR threshold
Max Drawdown: Largest peak-to-trough decline
Sharpe: (Return - RFR) / Volatility - Risk-adjusted returns (>1 good, >2 excellent)

Stablecoin Modeling

Balance Sheet:

• Assets: Cash reserves, spot collateral, derivative hedges
• Liabilities: Stablecoin supply
• Equity: Insurance fund, protocol reserves

Key Ratios:

Collateral_Ratio = Total_Assets / Stablecoin_Supply  (>100% = overcollateralized)
Coverage_Ratio = (Cash + Insurance) / Supply  (immediate redemption capacity)

Delta-Neutral Stablecoin: Hold volatile collateral (ETH/BTC), hedge with short perps (Δ≈0), generate yield from funding arbitrage.

Trade-offs: Capital efficient vs. cash reserves, funding income potential vs. liquidation/basis/counterparty risks.

Installation

pip install -e ".[dev]"

Running the Dashboard

streamlit run app.py

The dashboard provides an interactive interface to:

• Configure delta-neutral trading strategies or stablecoin portfolios
• Run Monte Carlo simulations
• Visualize risk metrics, equity curves, and scenarios
• Analyze VaR, drawdowns, and liquidation risk