from __future__ import annotations

from datetime import date, timedelta
from typing import Literal

import QuantLib as ql

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

DEFAULT_RISK_FREE_RATE: float = 0.045
DEFAULT_VOLATILITY_GUESS: float = 0.16
DEFAULT_DIVIDEND_YIELD: float = 0.0


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) -> ql.Option.Type:
    return ql.Option.Call if option_type == "call" else ql.Option.Put


def implied_volatility(
    option_price: float,
    spot: float,
    strike: float,
    time_to_expiry: float,
    risk_free_rate: float = DEFAULT_RISK_FREE_RATE,
    option_type: OptionType = "put",
    dividend_yield: float = DEFAULT_DIVIDEND_YIELD,
    valuation_date: date | None = None,
    initial_guess: float = DEFAULT_VOLATILITY_GUESS,
    min_vol: float = 1e-4,
    max_vol: float = 4.0,
    accuracy: float = 1e-8,
    max_evaluations: int = 500,
) -> float:
    """Invert the Black-Scholes-Merton model to solve for implied volatility.

    Assumptions:
        - European option exercise
        - Flat rate, dividend, and volatility term structures
        - GLD dividend yield defaults to zero

    Args:
        option_price: Observed market premium.
        spot: Current underlying price.
        strike: Option strike price.
        time_to_expiry: Time to maturity in years.
        risk_free_rate: Annual risk-free rate.
        option_type: ``"call"`` or ``"put"``.
        dividend_yield: Continuous dividend yield.
        valuation_date: Pricing date, defaults to today.
        initial_guess: Starting volatility guess used in the pricing process.
        min_vol: Lower volatility search bound.
        max_vol: Upper volatility search bound.
        accuracy: Root-finding tolerance.
        max_evaluations: Maximum solver iterations.

    Returns:
        The annualized implied volatility as a decimal.

    Example:
        >>> vol = implied_volatility(
        ...     option_price=12.0,
        ...     spot=460.0,
        ...     strike=430.0,
        ...     time_to_expiry=0.5,
        ...     risk_free_rate=0.045,
        ...     option_type="put",
        ... )
        >>> vol > 0
        True
    """

    if option_price <= 0 or spot <= 0 or strike <= 0 or time_to_expiry <= 0:
        raise ValueError("option_price, spot, strike, and time_to_expiry must be positive")
    if initial_guess <= 0 or min_vol <= 0 or max_vol <= min_vol:
        raise ValueError("invalid volatility bounds or initial_guess")

    option_type = _validate_option_type(option_type)
    valuation = valuation_date or date.today()
    maturity = valuation + timedelta(days=max(1, round(time_to_expiry * 365)))

    valuation_ql = ql.Date(valuation.day, valuation.month, valuation.year)
    maturity_ql = ql.Date(maturity.day, maturity.month, maturity.year)
    ql.Settings.instance().evaluationDate = valuation_ql

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

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

    process = ql.BlackScholesMertonProcess(
        spot_handle,
        dividend_curve,
        risk_free_curve,
        volatility_curve,
    )

    payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), strike)
    exercise = ql.EuropeanExercise(maturity_ql)
    option = ql.VanillaOption(payoff, exercise)
    option.setPricingEngine(ql.AnalyticEuropeanEngine(process))

    return float(
        option.impliedVolatility(
            option_price,
            process,
            accuracy,
            max_evaluations,
            min_vol,
            max_vol,
        )
    )