sentiment-engine/MALKHUT/malkhut/cwm/adverse_selection.py

"""
Adverse Selection Cost Model — quantify the cost of being picked off.

Measures:
  - Expected adverse selection cost per quote
  - Cost of being at the front of a toxic queue
  - Optimal quote placement to minimize adverse selection
"""
from __future__ import annotations

import math
from dataclasses import dataclass
from typing import Optional, Tuple

import numpy as np
from numba import njit


@dataclass(frozen=True, slots=True)
class AdverseSelectionCost:
    """Components of adverse selection cost."""
    expected_cost_bps: float  # expected cost in basis points
    pick_off_probability: float  # probability of being picked off
    toxic_flow_fraction: float  # fraction of fills that are toxic
    queue_position_risk: float  # risk from queue position


@njit(cache=True)
def compute_adverse_selection_cost(
    spread_bps: float,
    toxicity: float,
    queue_position: int,
    recent_trade_rate: float,
    quote_size_fraction: float,
    time_horizon_s: float,
) -> float:
    """
    Compute expected adverse selection cost in basis points.

    Model:
      - Base cost = spread_bps * pick_off_probability
      - Pick-off probability increases with toxicity and queue position
      - Cost is proportional to quote size

    Returns expected cost in basis points.
    """
    if spread_bps <= 0 or toxicity <= 0:
        return 0.0

    # Pick-off probability: higher toxicity = more likely to be picked off
    pick_off_prob = min(1.0, toxicity * 1.5)

    # Queue position factor: front of queue = higher pick-off risk
    queue_factor = 1.0 / (1.0 + queue_position * 0.1)

    # Expected adverse selection cost
    base_cost = spread_bps * pick_off_prob * queue_factor

    # Scale by quote size
    size_factor = quote_size_fraction

    return base_cost * size_factor


@njit(cache=True)
def compute_toxic_fill_ratio(
    fills: np.ndarray,
    fill_times: np.ndarray,
    toxicity_threshold: float,
) -> float:
    """
    Compute ratio of toxic fills.

    A fill is "toxic" if the price moves adversely after the fill.
    Simplified: fill is toxic if toxicity > threshold at time of fill.

    Returns 0.0-1.0 ratio.
    """
    if len(fills) == 0:
        return 0.0
    toxic_count = 0
    for i in range(len(fills)):
        if fills[i] > toxicity_threshold:
            toxic_count += 1
    return toxic_count / len(fills)


@njit(cache=True)
def optimal_quote_offset(
    spread_bps: float,
    toxicity: float,
    queue_depth: float,
    our_qty: float,
    recent_trade_rate: float,
) -> int:
    """
    Compute optimal quote offset (ticks from best) to minimize adverse selection.

    Model:
      - Offset 0 (best bid/ask): highest fill probability, highest adverse selection
      - Offset 1+: lower fill probability, lower adverse selection
      - Optimal offset balances fill probability vs adverse selection cost

    Returns optimal offset in ticks.
    """
    if spread_bps <= 0 or toxicity <= 0:
        return 0

    best_offset = 0
    best_score = -float("inf")

    for offset in range(5):  # check offsets 0-4
        # Fill probability decreases with offset
        fill_prob = max(0.0, 1.0 - offset * 0.2)

        # Adverse selection cost decreases with offset
        adverse_cost = spread_bps * toxicity * max(0.0, 1.0 - offset * 0.3)

        # Score: maximize fill probability minus adverse cost
        score = fill_prob - adverse_cost * 0.1

        if score > best_score:
            best_score = score
            best_offset = offset

    return best_offset


class AdverseSelectionModel:
    """
    Adverse selection cost model for the CWM.

    Integrates with queue model and spread dynamics to provide:
      - Expected adverse selection cost per quote
      - Optimal quote placement
      - Toxic fill ratio tracking
    """

    def __init__(self) -> None:
        self._toxic_fills: list[float] = []
        self._total_fills: int = 0

    def compute_cost(
        self,
        spread_bps: float,
        toxicity: float,
        queue_position: int,
        recent_trade_rate: float = 0.5,
        quote_size_fraction: float = 0.25,
        time_horizon_s: float = 300.0,
    ) -> AdverseSelectionCost:
        """Compute adverse selection cost for a quote."""
        cost_bps = compute_adverse_selection_cost(
            spread_bps, toxicity, queue_position, recent_trade_rate,
            quote_size_fraction, time_horizon_s,
        )
        pick_off_prob = min(1.0, toxicity * 1.5) * (1.0 / (1.0 + queue_position * 0.1))
        toxic_frac = self.toxic_fill_ratio

        return AdverseSelectionCost(
            expected_cost_bps=cost_bps,
            pick_off_probability=pick_off_prob,
            toxic_flow_fraction=toxic_frac,
            queue_position_risk=1.0 / (1.0 + queue_position * 0.1),
        )

    def optimal_offset(
        self,
        spread_bps: float,
        toxicity: float,
        queue_depth: float = 1.0,
        our_qty: float = 0.001,
        recent_trade_rate: float = 0.5,
    ) -> int:
        """Compute optimal quote offset."""
        return optimal_quote_offset(spread_bps, toxicity, queue_depth, our_qty, recent_trade_rate)

    def record_fill(self, toxicity: float) -> None:
        """Record a fill for toxic fill ratio tracking."""
        self._toxic_fills.append(toxicity)
        self._total_fills += 1

    @property
    def toxic_fill_ratio(self) -> float:
        if self._total_fills == 0:
            return 0.0
        return sum(1 for t in self._toxic_fills if t > 0.5) / self._total_fills

    @property
    def average_toxicity(self) -> float:
        if not self._toxic_fills:
            return 0.0
        return sum(self._toxic_fills) / len(self._toxic_fills)