O(1) SIMM

Introduction to ISDA SIMM concept :

Introduction to SIMMFrom First Principles

1. PSIM for PIO Standard Initial Margin, a DeFi IRDs and DeFi Derivative Oriented ISDA SIMM inspired and adapted to blockchain constraints.

Key benefits of PSIM implementation:

1. By accounting for correlations between assets, PSIM can potentially reduce margin requirements without compromising on safety.

2. PSIM implementation is suited for optimizing margin requirements for IRDs which are capital-intensive but low-risk products. IRDs are not present yet in DeFi as the market is too immature and volatile, this is a chicken and egg problem where derivatives bring stability and liquidity to a market.

PSIM High IM Gains Example :

PSIM ( PIO Standart Initial Margin )
|
|-- Crypto Derivatives (IM: $1,200k, MPOR: 15 days, Floor: $250k, Gained IM (RW & Corr): $800k (67%))
|   Div: -$120k, Conc: $100k
|   |
|   |-- Crypto Futures and Curvature (IM: $700k, Floor: $130k, Gained IM (RW & Corr): $420k (60%))
|   |   Div: -$80k, Conc: $70k
|   |   |
|   |   |-- Crypto Futures Volatility (IM: $450k, Liquidity Horizon: 90 days, Floor: $90k, Gained IM (RW & Corr): $270k (60%))
|   |   |   Div: -$50k, Conc: $40k
|   |   |   |-- USDC [OI: $900k, IM: $225k, RW: 0.25, Corr: EUR(0.98), WETH(0.1), WBTC(0.1)]
|   |   |   |-- EUR [OI: $700k, IM: $175k, RW: 0.25, Corr: USDC(0.98), WETH(0.1), WBTC(0.1)]
|   |   |   |-- WETH [OI: $500k, IM: $200k, RW: 0.4, Corr: USDC(0.1), EUR(0.1), WBTC(0.95)]
|   |   |   |-- WBTC [OI: $300k, IM: $135k, RW: 0.45, Corr: USDC(0.1), EUR(0.1), WETH(0.95)]
|   |   |
|   |   |-- Crypto Curvature (IM: $250k, Liquidity Horizon: 60 days, Floor: $50k, Gained IM (RW & Corr): $150k (60%))
|   |       Div: -$30k, Conc: $25k
|   |       |-- USDC [OI: $500k, IM: $125k, RW: 0.25, Corr: EUR(0.95), WETH(0.15), WBTC(0.15)]
|   |       |-- EUR [OI: $400k, IM: $100k, RW: 0.25, Corr: USDC(0.95), WETH(0.15), WBTC(0.15)]
|   |       |-- WETH [OI: $250k, IM: $100k, RW: 0.4, Corr: USDC(0.15), EUR(0.15), WBTC(0.9)]
|   |       |-- WBTC [OI: $150k, IM: $67.5k, RW: 0.45, Corr: USDC(0.15), EUR(0.15), WETH(0.9)]
|   
|-- DeFi Derivatives (IM: $2,500k, MPOR: 30 days, Floor: $500k, Gained IM (RW & Corr): $2,250k (90%))
    Div: -$300k, Conc: $250k
    |
    |-- AMM Swap Yield on Pool (IM: $1,500k, Floor: $300k, Gained IM (RW & Corr): $1,350k (90%))
    |   Div: -$200k, Conc: $150k
    |   |
    |   |-- AMM Swap Yield Volatility (IM: $1,500k, Liquidity Horizon: 60 days, Floor: $300k, Gained IM (RW & Corr): $1,350k (90%))
    |       Div: -$200k, Conc: $150k
    |       |-- Uniswap vs Curve WBTC/WETH [OI: $2,500k, IM: $875k, RW: 0.35, Corr: Uniswap vs PancakeSwap WBTC/WETH(0.85), Uniswap vs Balancer WETH/STETH(0.8)]
    |       |-- Uniswap vs PancakeSwap WBTC/WETH [OI: $2,000k, IM: $700k, RW: 0.35, Corr: Uniswap vs Curve WBTC/WETH(0.85), Uniswap vs Balancer WETH/STETH(0.75)]
    |       |-- Uniswap vs Balancer WETH/STETH [OI: $1,500k, IM: $600k, RW: 0.4, Corr: Uniswap vs Curve WBTC/WETH(0.8), Uniswap vs PancakeSwap WBTC/WETH(0.75)]
    |
    |-- IR Swaps on Staking (IM: $750k, Floor: $150k, Gained IM (RW & Corr): $675k (90%))
    |   Div: -$75k, Conc: $60k
    |   |
    |   |-- IR Swaps on Staking Volatility (IM: $750k, Liquidity Horizon: 90 days, Floor: $150k, Gained IM (RW & Corr): $675k (90%))
    |       Div: -$75k, Conc: $60k
    |       |-- Lido vs RocketPool [OI: $3,000k, IM: $450k, RW: 0.15, Corr: Lido vs Mantle(0.95), RocketPool vs Mantle(0.9)]
    |       |-- Lido vs Mantle [OI: $2,500k, IM: $375k, RW: 0.15, Corr: Lido vs RocketPool(0.95), RocketPool vs Mantle(0.9)]
    |       |-- RocketPool vs Mantle [OI: $2,000k, IM: $300k, RW: 0.15, Corr: Lido vs RocketPool(0.9), Lido vs Mantle(0.9)]
    |
    |-- Lending Yield (IM: $250k, Floor: $50k, Gained IM (RW & Corr): $225k (90%))
        Div: -$25k, Conc: $20k
        |
        |-- Lending Yield Volatility (IM: $250k, Liquidity Horizon: 60 days, Floor: $50k, Gained IM (RW & Corr): $225k (90%))
            Div: -$25k, Conc: $20k
            |-- Aave WETH vs Fix [OI: $1,000k, IM: $150k, RW: 0.15, Corr: Spark WBTC vs Compound WBTC(0.9)]
            |-- Spark WBTC vs Compound WBTC [OI: $800k, IM: $120k, RW: 0.15, Corr: Aave WETH vs Fix(0.9)]

Total Diversification IM: -$420k
Total Concentration IM: $350k
Total Gained IM (RW & Corr): $3,050k (82%)

Total IM = Crypto Derivatives IM + DeFi Derivatives IM + Total Diversification IM + Total Concentration IM
         = $1,200k + $2,500k - $420k + $350k

                  = $3,630k

Local-only PSIM computation :

1. Each time a trade is updated, a subset of intermediary variables is updated.

2. PSIM is decomposed into step computation with sums only that are stored, updated, and used to compute the total result.

1. PIO comprises bilateral and semi-multilateral contracts, which cannot be computed as a whole due to blockchain-restricted computing capabilities. An O(nlogn) solution is incompatible with a n asset portfolio.