import numpy as np
from scipy.stats import norm
from typing import Dict, Any, List, Optional
from datetime import datetime, timedelta
import math


def black_scholes(
    S: float, K: float, T: float, r: float, sigma: float, option_type: str = "call",
    include_second_order: bool = True,
) -> Dict[str, float]:
    """Black-Scholes pricing + Greeks (first-order delta/gamma/theta/vega/rho, plus the
    second-order Greeks used by Strategy Builder's "advanced sensitivities" panel: vanna,
    charm, vomma/volga, veta, speed, color, zomma — vera deliberately omitted, see project
    memory "Strategy Builder Greeks plan"). All second-order values are scaled to match the
    convention their related first-order Greek already uses here — e.g. vanna/vomma/zomma
    are "per vol POINT" like vega already is (not per unit of raw decimal sigma), charm/
    color/veta are "per DAY" like theta already is (not per year) — every formula/scaling
    is verified against finite-difference bumps of this same function's own first-order
    outputs (see scratchpad test_second_order_greeks.py from the Phase 3 build), not just
    hand-derived from a textbook, since these third-derivative formulas are easy to get
    subtly wrong.

    `include_second_order=False` skips that block entirely — strategy_engine.value_at()
    (the workhorse of check_bounded_risk's ~700-point grid search per candidate, itself
    called for every candidate the optimizer scans) only ever reads `["price"]`, so paying
    for 7 unused derivatives on every one of those hundreds of thousands of calls was pure
    waste discovered while profiling the Phase 4 retrospective-comparison feature — this
    flag is what fixed it, not a hypothetical optimization."""
    S = float(S or 100.0)
    K = float(K or S)
    T = float(T or 0.001)
    sigma = float(sigma or 0.25)
    if T <= 0 or sigma <= 0:
        intrinsic = max(0, S - K) if option_type == "call" else max(0, K - S)
        result = {"price": intrinsic, "delta": 0, "gamma": 0, "theta": 0, "vega": 0, "rho": 0}
        if include_second_order:
            result.update({"vanna": 0, "charm": 0, "vomma": 0, "veta": 0, "speed": 0, "color": 0, "zomma": 0})
        return result

    sqrtT = math.sqrt(T)
    d1 = (math.log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrtT)
    d2 = d1 - sigma * sqrtT
    phi_d1 = norm.pdf(d1)

    if option_type == "call":
        price = S * norm.cdf(d1) - K * math.exp(-r * T) * norm.cdf(d2)
        delta = norm.cdf(d1)
        rho = K * T * math.exp(-r * T) * norm.cdf(d2) / 100
    else:
        price = K * math.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
        delta = norm.cdf(d1) - 1
        rho = -K * T * math.exp(-r * T) * norm.cdf(-d2) / 100

    gamma = phi_d1 / (S * sigma * sqrtT)
    theta = (-(S * phi_d1 * sigma) / (2 * sqrtT) - r * K * math.exp(-r * T) * norm.cdf(d2 if option_type == "call" else -d2)) / 365
    vega = S * phi_d1 * sqrtT / 100

    result = {
        "price": round(price, 4),
        "delta": round(delta, 4),
        "gamma": round(gamma, 6),
        "theta": round(theta, 4),
        "vega": round(vega, 4),
        "rho": round(rho, 4),
    }
    if not include_second_order:
        return result

    # Second-order — same for calls and puts (this pricer carries no dividend yield, so the
    # extra q-term that would otherwise make charm/veta/color differ by option_type is zero).
    vanna = (-phi_d1 * d2 / sigma) / 100
    vomma = (S * phi_d1 * sqrtT * d1 * d2 / sigma) / 10_000
    charm = (-phi_d1 * (2 * r * T - d2 * sigma * sqrtT) / (2 * T * sigma * sqrtT)) / 365
    veta = (S * phi_d1 * sqrtT * ((r * d1) / (sigma * sqrtT) - (1 + d1 * d2) / (2 * T))) / 36_500
    speed = -(gamma / S) * (d1 / (sigma * sqrtT) + 1)
    color = (phi_d1 / (2 * S * T * sigma * sqrtT) * (2 * r * T + 1 + d1 * (2 * r * T - d2 * sigma * sqrtT) / (sigma * sqrtT))) / 365
    zomma = (gamma * (d1 * d2 - 1) / sigma) / 100

    result.update({
        "vanna": round(vanna, 6),
        "charm": round(charm, 6),
        "vomma": round(vomma, 6),
        "veta": round(veta, 6),
        "speed": round(speed, 8),
        "color": round(color, 8),
        "zomma": round(zomma, 6),
    })
    return result


def compute_pnl_curve(
    S: float, K: float, T: float, r: float, sigma: float,
    option_type: str, quantity: int, premium_paid: float
) -> List[Dict[str, float]]:
    """P&L at expiry across a range of underlying prices."""
    prices = np.linspace(S * 0.5, S * 1.5, 100)
    curve = []
    for price in prices:
        if option_type == "call":
            intrinsic = max(0, price - K)
        else:
            intrinsic = max(0, K - price)
        pnl = (intrinsic - premium_paid) * quantity * 100
        curve.append({"underlying": round(float(price), 2), "pnl": round(float(pnl), 2)})
    return curve


def bull_call_spread(S: float, K_low: float, K_high: float, T: float, r: float, sigma: float) -> Dict[str, Any]:
    long_call = black_scholes(S, K_low, T, r, sigma, "call")
    short_call = black_scholes(S, K_high, T, r, sigma, "call")
    net_debit = long_call["price"] - short_call["price"]
    max_gain = (K_high - K_low) - net_debit
    return {
        "strategy": "Bull Call Spread",
        "net_debit": round(net_debit, 4),
        "max_loss": round(net_debit * 100, 2),
        "max_gain": round(max_gain * 100, 2),
        "breakeven": round(K_low + net_debit, 2),
        "legs": [
            {"type": "long call", "strike": K_low, "premium": long_call["price"]},
            {"type": "short call", "strike": K_high, "premium": short_call["price"]},
        ],
    }


def bear_put_spread(S: float, K_high: float, K_low: float, T: float, r: float, sigma: float) -> Dict[str, Any]:
    long_put = black_scholes(S, K_high, T, r, sigma, "put")
    short_put = black_scholes(S, K_low, T, r, sigma, "put")
    net_debit = long_put["price"] - short_put["price"]
    max_gain = (K_high - K_low) - net_debit
    return {
        "strategy": "Bear Put Spread",
        "net_debit": round(net_debit, 4),
        "max_loss": round(net_debit * 100, 2),
        "max_gain": round(max_gain * 100, 2),
        "breakeven": round(K_high - net_debit, 2),
        "legs": [
            {"type": "long put", "strike": K_high, "premium": long_put["price"]},
            {"type": "short put", "strike": K_low, "premium": short_put["price"]},
        ],
    }


def long_straddle(S: float, K: float, T: float, r: float, sigma: float) -> Dict[str, Any]:
    call = black_scholes(S, K, T, r, sigma, "call")
    put = black_scholes(S, K, T, r, sigma, "put")
    total_premium = call["price"] + put["price"]
    return {
        "strategy": "Long Straddle",
        "net_debit": round(total_premium, 4),
        "max_loss": round(total_premium * 100, 2),
        "max_gain": None,
        "breakevens": [round(K - total_premium, 2), round(K + total_premium, 2)],
        "legs": [
            {"type": "long call", "strike": K, "premium": call["price"]},
            {"type": "long put", "strike": K, "premium": put["price"]},
        ],
    }


def implied_vol_surface(S: float, strikes_pct: List[float], expiries_days: List[int], r: float, base_sigma: float) -> List[Dict]:
    """Generate a simplified IV surface (skew + term structure)."""
    surface = []
    for days in expiries_days:
        T = days / 365
        for pct in strikes_pct:
            K = S * pct
            moneyness = math.log(K / S)
            skew_adj = -0.3 * moneyness  # typical negative skew
            term_adj = 0.02 * math.sqrt(30 / max(days, 1))
            iv = max(0.05, base_sigma + skew_adj + term_adj)
            surface.append({"expiry_days": days, "strike_pct": pct, "strike": round(K, 2), "iv": round(iv, 4)})
    return surface