Simulation Engine

The simulation engine computes expected PnL for a specific position, incorporating all model adjustments.

Simulation Pipeline

Input Parameters
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1. Gross Funding PnL
     ↓
2. Decay Adjustment
     ↓
3. Survivability Adjustment
     ↓
4. Capacity Adjustment
     ↓
5. Fee Deduction
     ↓
Net Expected PnL

Input Parameters

Parameter	Symbol	Description
Position Size	$P$	USD notional
Holding Horizon	$h$	Hours
Entry Fee	$F_{entry}$	Basis points
Exit Fee	$F_{exit}$	Basis points

Step 1: Gross Funding PnL

Raw expected funding over the holding period:

PnL_{gross} = APR_f \times P \times \frac{h}{8760}

Where 8760 = hours per year.

Step 2: Decay Adjustment

Apply the decay factor for the holding horizon:

PnL_{decay} = PnL_{gross} \times D(h)

Where:

D(h) = \frac{1 - e^{-\lambda h}}{\lambda h}

Step 3: Survivability Adjustment

Apply the survivability score:

PnL_{surv} = PnL_{decay} \times \frac{S}{100}

Or equivalently using mirage ratio:

PnL_{surv} = PnL_{decay} \times (1 - M)

Step 4: Capacity Adjustment

Apply the capacity penalty:

PnL_{cap} = PnL_{surv} \times P_{cap}

Where:

P_{cap} = \min\left(1, \frac{C_{soft}}{P}\right)^{\gamma}

Step 5: Fee Deduction

Calculate total fees:

F_{total} = P \times \frac{F_{entry} + F_{exit}}{10000}

Final net PnL:

PnL_{net} = PnL_{cap} - F_{total}

Net Expected Return

As a percentage of position size:

R_{net} = \frac{PnL_{net}}{P} \times 100

Complete Example

Inputs:

$APR_f = 150\%$
Position $P = 20{,}000$ USD
Horizon $h = 48$ hours
Entry fee = 5 bps
Exit fee = 5 bps
$t_{half} = 36$ hours
Survivability $S = 70$
$C_{soft} = 30{,}000$ USD

Step 1: Gross PnL

PnL_{gross} = 1.50 \times 20000 \times \frac{48}{8760} = 164.38

Step 2: Decay Adjustment

$\lambda = \ln(2) / 36 = 0.0193$
$D(48) = (1 - e^{-0.0193 \times 48}) / (0.0193 \times 48) = 0.62$

PnL_{decay} = 164.38 \times 0.62 = 101.92

Step 3: Survivability

PnL_{surv} = 101.92 \times 0.70 = 71.34

Step 4: Capacity

Position (20k) is less than $C_{soft}$ (30k), so $P_{cap} = 1.0$

PnL_{cap} = 71.34 \times 1.0 = 71.34

Step 5: Fees

F_{total} = 20000 \times \frac{5 + 5}{10000} = 20.00

Final Result:

PnL_{net} = 71.34 - 20.00 = 51.34

R_{net} = \frac{51.34}{20000} \times 100 = 0.257\%

Breakeven Analysis

The simulation can identify:

Breakeven horizon — Minimum holding time for positive returns
Breakeven size — Maximum position before fees consume all returns
Optimal horizon — Holding period maximizing return %

Capacity Model Trust Layer