from __future__ import annotations

from dataclasses import dataclass
from datetime import date, timedelta
import math
from typing import Any, Literal

try:  # pragma: no cover - optional dependency
    import QuantLib as ql
except ImportError:  # pragma: no cover - optional dependency
    ql = None

OptionType = Literal["call", "put"]

DEFAULT_GOLD_PRICE_PER_OUNCE: float = 4600.0
DEFAULT_GLD_PRICE: float = 460.0
DEFAULT_RISK_FREE_RATE: float = 0.045
DEFAULT_VOLATILITY: float = 0.16
DEFAULT_DIVIDEND_YIELD: float = 0.0


@dataclass(frozen=True)
class BlackScholesInputs:
    """Inputs for European Black-Scholes pricing."""

    spot: float = DEFAULT_GLD_PRICE
    strike: float = DEFAULT_GLD_PRICE
    time_to_expiry: float = 0.25
    risk_free_rate: float = DEFAULT_RISK_FREE_RATE
    volatility: float = DEFAULT_VOLATILITY
    option_type: OptionType = "put"
    dividend_yield: float = DEFAULT_DIVIDEND_YIELD
    valuation_date: date | None = None


@dataclass(frozen=True)
class PricingResult:
    """European option price and Greeks."""

    price: float
    delta: float
    gamma: float
    theta: float
    vega: float
    rho: float


@dataclass(frozen=True)
class HedgingCost:
    """Annualized hedging cost summary."""

    premium_paid: float
    annual_cost_dollars: float
    annual_cost_pct: float


def _validate_option_type(option_type: str) -> OptionType:
    option = option_type.lower()
    if option not in {"call", "put"}:
        raise ValueError("option_type must be either 'call' or 'put'")
    return option  # type: ignore[return-value]


def _to_quantlib_option_type(option_type: OptionType) -> Any:
    if ql is None:
        raise RuntimeError("QuantLib is not installed")
    return ql.Option.Call if option_type == "call" else ql.Option.Put


def _build_dates(time_to_expiry: float, valuation_date: date | None) -> tuple[Any, Any]:
    if time_to_expiry <= 0.0:
        raise ValueError("time_to_expiry must be positive")
    if ql is None:
        return (None, None)

    valuation = valuation_date or date.today()
    maturity = valuation + timedelta(days=max(1, round(time_to_expiry * 365)))
    return (
        ql.Date(valuation.day, valuation.month, valuation.year),
        ql.Date(maturity.day, maturity.month, maturity.year),
    )


def _norm_pdf(value: float) -> float:
    return math.exp(-(value**2) / 2.0) / math.sqrt(2.0 * math.pi)


def _norm_cdf(value: float) -> float:
    return 0.5 * (1.0 + math.erf(value / math.sqrt(2.0)))


def _analytic_black_scholes(params: BlackScholesInputs, option_type: OptionType) -> PricingResult:
    if params.spot <= 0 or params.strike <= 0 or params.time_to_expiry <= 0 or params.volatility <= 0:
        raise ValueError("spot, strike, time_to_expiry, and volatility must be positive")

    t = params.time_to_expiry
    sigma = params.volatility
    sqrt_t = math.sqrt(t)
    d1 = (
        math.log(params.spot / params.strike)
        + (params.risk_free_rate - params.dividend_yield + 0.5 * sigma**2) * t
    ) / (sigma * sqrt_t)
    d2 = d1 - sigma * sqrt_t
    disc_r = math.exp(-params.risk_free_rate * t)
    disc_q = math.exp(-params.dividend_yield * t)
    pdf_d1 = _norm_pdf(d1)

    if option_type == "call":
        price = params.spot * disc_q * _norm_cdf(d1) - params.strike * disc_r * _norm_cdf(d2)
        delta = disc_q * _norm_cdf(d1)
        theta = (
            -(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
            - params.risk_free_rate * params.strike * disc_r * _norm_cdf(d2)
            + params.dividend_yield * params.spot * disc_q * _norm_cdf(d1)
        )
        rho = params.strike * t * disc_r * _norm_cdf(d2)
    else:
        price = params.strike * disc_r * _norm_cdf(-d2) - params.spot * disc_q * _norm_cdf(-d1)
        delta = disc_q * (_norm_cdf(d1) - 1.0)
        theta = (
            -(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
            + params.risk_free_rate * params.strike * disc_r * _norm_cdf(-d2)
            - params.dividend_yield * params.spot * disc_q * _norm_cdf(-d1)
        )
        rho = -params.strike * t * disc_r * _norm_cdf(-d2)

    gamma = (disc_q * pdf_d1) / (params.spot * sigma * sqrt_t)
    vega = params.spot * disc_q * pdf_d1 * sqrt_t
    return PricingResult(price=float(price), delta=float(delta), gamma=float(gamma), theta=float(theta), vega=float(vega), rho=float(rho))


def black_scholes_price_and_greeks(params: BlackScholesInputs) -> PricingResult:
    """Price a European option with QuantLib when available, otherwise analytic BSM."""

    option_type = _validate_option_type(params.option_type)
    if ql is None:
        return _analytic_black_scholes(params, option_type)

    valuation_ql, maturity_ql = _build_dates(params.time_to_expiry, params.valuation_date)
    ql.Settings.instance().evaluationDate = valuation_ql

    day_count = ql.Actual365Fixed()
    calendar = ql.NullCalendar()

    spot_handle = ql.QuoteHandle(ql.SimpleQuote(params.spot))
    dividend_curve = ql.YieldTermStructureHandle(
        ql.FlatForward(valuation_ql, params.dividend_yield, day_count)
    )
    risk_free_curve = ql.YieldTermStructureHandle(
        ql.FlatForward(valuation_ql, params.risk_free_rate, day_count)
    )
    volatility = ql.BlackVolTermStructureHandle(
        ql.BlackConstantVol(valuation_ql, calendar, params.volatility, day_count)
    )

    process = ql.BlackScholesMertonProcess(spot_handle, dividend_curve, risk_free_curve, volatility)
    payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), params.strike)
    exercise = ql.EuropeanExercise(maturity_ql)
    option = ql.VanillaOption(payoff, exercise)
    option.setPricingEngine(ql.AnalyticEuropeanEngine(process))

    return PricingResult(
        price=float(option.NPV()),
        delta=float(option.delta()),
        gamma=float(option.gamma()),
        theta=float(option.theta()),
        vega=float(option.vega()),
        rho=float(option.rho()),
    )


def margin_call_threshold_price(
    portfolio_value: float,
    loan_amount: float,
    current_price: float = DEFAULT_GLD_PRICE,
    margin_call_ltv: float = 0.75,
) -> float:
    """Calculate the underlying price where a margin call is triggered."""

    if portfolio_value <= 0 or loan_amount <= 0 or current_price <= 0:
        raise ValueError("portfolio_value, loan_amount, and current_price must be positive")
    if not 0 < margin_call_ltv < 1:
        raise ValueError("margin_call_ltv must be between 0 and 1")

    units = portfolio_value / current_price
    return loan_amount / (margin_call_ltv * units)


def annual_hedging_cost(
    premium_per_share: float,
    shares_hedged: float,
    portfolio_value: float,
    hedge_term_years: float,
) -> HedgingCost:
    """Annualize the premium cost of a hedging program."""

    if premium_per_share < 0 or shares_hedged <= 0 or portfolio_value <= 0 or hedge_term_years <= 0:
        raise ValueError(
            "premium_per_share must be non-negative and shares_hedged, portfolio_value, "
            "and hedge_term_years must be positive"
        )

    premium_paid = premium_per_share * shares_hedged
    annual_cost_dollars = premium_paid / hedge_term_years
    annual_cost_pct = annual_cost_dollars / portfolio_value
    return HedgingCost(
        premium_paid=premium_paid,
        annual_cost_dollars=annual_cost_dollars,
        annual_cost_pct=annual_cost_pct,
    )