Market Maker Inventory and Mark-to-Market PnL Event Simulator

Market maker performance tracking at Optiver and Jump Trading requires real-time attribution of cash balances, FIFO inventory matching, and Mark-to-Market (MTM) PnL across rapid event streams.

Design an automated market maker accounting simulator MarketMakerSimulator that processes a chronological sequence of trade executions and mid-price updates.

Accounting Rules:

1. Cash Accounting: A buy of volume $V$ at price $P$ reduces cash by $P \cdot V$. A sell increases cash by $P \cdot V$.
2. FIFO Inventory Tranches: Inventory is matched on a First-In-First-Out (FIFO) basis. When holding long inventory, selling shares closes the oldest long tranche, realizing profit $(P_{sell} - P_{buy}) \cdot V$. Conversely, when holding short inventory, buying shares covers the oldest short tranche, realizing profit $(P_{short} - P_{buy}) \cdot V$.
3. Mark-to-Market PnL: At any benchmark mid-price $P_{mid}$: $\text{MTM PnL} = \text{Cash} + (\text{Inventory} \times P_{mid}) - \text{Initial Cash}$

Your Task

Implement the MarketMakerSimulator class:

• __init__(initial_cash: float = 0.0)
• record_fill(timestamp: float, side: str, price: float, volume: int) -> None (side is 'buy' or 'sell')
• update_mid_price(timestamp: float, mid_price: float) -> None
• get_summary() -> dict returning {'cash': float, 'inventory': int, 'realized_pnl': float, 'unrealized_pnl': float, 'mtm_pnl': float}.

Constraints

• All prices $> 0.0$, volumes $\ge 1$.
• All calculations rounded to 4 decimal places in summary.