libitofin 0.49.0

//! Monte Carlo American-option engine.
//!
//! Port of `ql/pricingengines/vanilla/mcamericanengine.{hpp,cpp}`: the
//! Longstaff-Schwartz engine for American and Bermudan vanilla options.
//! [`AmericanPathPricer`] supplies the three things the backward induction needs
//! from the option (`mcamericanengine.cpp:31-72`), [`MCAmericanEngine`] wires it
//! into the two-pass [`McLongstaffSchwartzEngineBase`] driver, and
//! [`MakeMcAmericanEngine`] ports the `MakeMCAmericanEngine` factory
//! (`mcamericanengine.hpp:105`).
//!
//! The regression state is the spot SCALED by `1 / strike` (`:51,66`), for
//! numerical stability, while the exercise value is the payoff of the UNSCALED
//! spot (`:60`). The payoff itself is appended to the basis system as one extra
//! function (`:45-46`), so order `n` yields `n + 2` basis functions:
//! `{1, s, ..., s^n, payoff(s)}`, all evaluated at the scaled state.
//!
//! Divergences from `mcamericanengine.{hpp,cpp}`, all deliberate:
//! - **the striked-payoff scaling is unconditional**: C++ takes an
//!   `ext::shared_ptr<Payoff>` and only divides `scalingValue_` by the strike
//!   when the `dynamic_pointer_cast<StrikedTypePayoff>` succeeds (`:48-52`).
//!   `OptionArguments::payoff` is already a `StrikedTypePayoff` here, so the
//!   cast is a compile-time fact and the scaling is always `1 / strike`.
//! - **the process is concretely a [`GeneralizedBlackScholesProcess`]**, so the
//!   "generalized Black-Scholes process required" downcast
//!   (`mcamericanengine.hpp:190-193`) cannot fail at run time, as with
//!   [`MCEuropeanEngine`](super::MCEuropeanEngine).
//!
//! Bermudan exercise is restricted to contractual dates in both calibration
//! and pricing. QuantLib 1.43 instead permits exercise on refined simulation
//! nodes; this deliberate correction is covered by deterministic path and FD
//! oracles. All positive contractual dates remain mandatory simulation nodes.
//!
//! The control variate (`mcamericanengine.hpp:76-78`) is the European twin:
//! [`control_path_pricer`](MCAmericanEngine::control_path_pricer) prices the
//! discounted terminal payoff of each pricing path, and
//! [`control_variate_value`](MCAmericanEngine::control_variate_value) reprices
//! the option analytically with a European exercise on its last date. Under
//! the control variate the value is floored at zero (`:176-183`). The C++
//! "StrikedTypePayoff needed for control variate" downcast (`:214-217`) cannot
//! fail here, for the same reason as the scaling above.
//!
//! Deferred, rejected visibly rather than silently ignored:
//! - **the multi-asset `MCAmericanBasketEngine`**, needing the `MultiPath` form
//!   of the Longstaff-Schwartz pricer.

use std::any::Any;

use crate::errors::QlResult;
use crate::exercise::{EuropeanExercise, Exercise, ExerciseType};
use crate::instruments::{OneAssetOptionResults, OptionArguments, StrikedTypePayoff};
use crate::math::randomnumbers::rngtraits::McRngTraits;
use crate::methods::montecarlo::{
    ControlVariate, EarlyExercisePathPricer, LongstaffSchwartzPathPricer, LsmBasisSystem, Path,
    PolynomialType,
};
use crate::patterns::observable::{AsObservable, Observable};
use crate::pricingengine::{Arguments, PricingEngine, Results};
use crate::pricingengines::McLongstaffSchwartzEngineBase;
use crate::pricingengines::vanilla::{AnalyticEuropeanEngine, EuropeanPathPricer};
use crate::processes::GeneralizedBlackScholesProcess;
use crate::shared::{Shared, shared};
use crate::stochasticprocess::StochasticProcess1D;
use crate::types::{Real, Size};
use crate::{fail, require};

/// Values an American vanilla option along one realized path
/// (`mcamericanengine.cpp:31-72`).
pub struct AmericanPathPricer {
    payoff: Shared<dyn StrikedTypePayoff>,
    scaling_value: Real,
    polynomial_order: Size,
    polynomial_type: PolynomialType,
    exercise_indices: Option<Vec<bool>>,
}

impl AmericanPathPricer {
    /// Builds the pricer, scaling the regression state by `1 / strike`
    /// (`mcamericanengine.cpp:48-52`).
    pub fn new(
        payoff: Shared<dyn StrikedTypePayoff>,
        polynomial_order: Size,
        polynomial_type: PolynomialType,
    ) -> AmericanPathPricer {
        let scaling_value = 1.0 / payoff.strike();
        AmericanPathPricer {
            payoff,
            scaling_value,
            polynomial_order,
            polynomial_type,
            exercise_indices: None,
        }
    }
}

impl EarlyExercisePathPricer<Path> for AmericanPathPricer {
    type State = Real;

    /// The payoff of the UNSCALED spot (`mcamericanengine.cpp:55-61`). C++ round
    /// trips the state through the scaling rather than reading `path[t]`, and so
    /// does this, so the two agree to the last bit.
    fn value(&self, path: &Path, t: Size) -> Real {
        if self
            .exercise_indices
            .as_ref()
            .is_some_and(|indices| !indices[t])
        {
            return 0.0;
        }
        self.payoff.value(self.state(path, t) / self.scaling_value)
    }

    /// The spot scaled by `1 / strike` (`mcamericanengine.cpp:63-66`).
    fn state(&self, path: &Path, t: Size) -> Real {
        path[t] * self.scaling_value
    }

    /// The monomials plus the payoff as one extra function
    /// (`mcamericanengine.cpp:45-46`). The appended function takes the SCALED
    /// state and undoes the scaling before applying the payoff (`:57`).
    fn basis_system(&self) -> Vec<Box<dyn Fn(Real) -> Real>> {
        let mut v = LsmBasisSystem::path_basis_system(self.polynomial_order, self.polynomial_type);
        let payoff = Shared::clone(&self.payoff);
        let scaling_value = self.scaling_value;
        v.push(Box::new(move |state: Real| {
            payoff.value(state / scaling_value)
        }));
        v
    }
}

/// American vanilla Monte Carlo engine (`mcamericanengine.hpp:51`), generic over `RNG`.
pub struct MCAmericanEngine<RNG> {
    base: McLongstaffSchwartzEngineBase<RNG>,
    process: Shared<GeneralizedBlackScholesProcess>,
    polynomial_order: Size,
    polynomial_type: PolynomialType,
}

impl<RNG: McRngTraits> MCAmericanEngine<RNG> {
    /// Builds the engine (`mcamericanengine.hpp:140-172`), which fixes the
    /// Brownian bridge to `false` (`:161`). Prefer [`MakeMcAmericanEngine`].
    ///
    /// # Errors
    ///
    /// Propagates the driver's time-step validation.
    #[allow(clippy::too_many_arguments)]
    pub fn new(
        process: Shared<GeneralizedBlackScholesProcess>,
        time_steps: Option<Size>,
        time_steps_per_year: Option<Size>,
        antithetic_variate: bool,
        control_variate: bool,
        required_samples: Option<Size>,
        required_tolerance: Option<Real>,
        max_samples: Option<Size>,
        seed: u32,
        polynomial_order: Size,
        polynomial_type: PolynomialType,
        n_calibration_samples: Option<Size>,
        antithetic_variate_calibration: Option<bool>,
        seed_calibration: Option<u32>,
    ) -> QlResult<MCAmericanEngine<RNG>> {
        require!(
            !matches!(
                polynomial_type,
                PolynomialType::Legendre | PolynomialType::Chebyshev
            ),
            "insufficient polynomial type"
        );
        let base = McLongstaffSchwartzEngineBase::new(
            Shared::clone(&process) as Shared<dyn StochasticProcess1D>,
            time_steps,
            time_steps_per_year,
            false,
            antithetic_variate,
            control_variate,
            required_samples,
            required_tolerance,
            max_samples,
            seed,
            n_calibration_samples,
            antithetic_variate_calibration,
            seed_calibration,
        )?;
        Ok(MCAmericanEngine {
            base,
            process,
            polynomial_order,
            polynomial_type,
        })
    }

    /// The two-pass driver underneath, for the calibration settings it defaults.
    pub fn lsm_base(&self) -> &McLongstaffSchwartzEngineBase<RNG> {
        &self.base
    }

    /// The regression order the basis system is built to.
    pub fn polynomial_order(&self) -> Size {
        self.polynomial_order
    }

    /// The C++ `lsmPathPricer()` hook (`mcamericanengine.hpp:186-207`): a fresh
    /// [`LongstaffSchwartzPathPricer`] over an [`AmericanPathPricer`], discounted
    /// on the process risk-free curve.
    ///
    /// # Errors
    ///
    /// Errors on a missing payoff, a missing exercise, an exercise that is not
    /// American or Bermudan (`:196`), or one paying at expiry (`:197-198`); propagates a
    /// grid or discount failure. Chebyshev2nd call payoffs are rejected because
    /// their in-the-money states exceed the weighted basis domain.
    pub fn lsm_path_pricer(&self) -> QlResult<Shared<LongstaffSchwartzPathPricer>> {
        let arguments = self.base.arguments();
        let Some(exercise) = &arguments.exercise else {
            fail!("no exercise given");
        };
        require!(
            matches!(
                exercise.exercise_type(),
                ExerciseType::American | ExerciseType::Bermudan
            ),
            "wrong exercise given"
        );
        require!(!exercise.payoff_at_expiry(), "payoff at expiry not handled");
        let Some(payoff) = &arguments.payoff else {
            fail!("no payoff given");
        };

        require!(
            self.polynomial_type != PolynomialType::Chebyshev2nd
                || payoff.option_type() != crate::option::OptionType::Call,
            "Chebyshev2nd basis is undefined for in-the-money call states"
        );
        let grid = self.base.time_grid()?;
        let mut early = AmericanPathPricer::new(
            Shared::clone(payoff),
            self.polynomial_order,
            self.polynomial_type,
        );
        if exercise.exercise_type() == ExerciseType::Bermudan {
            let mut indices = vec![false; grid.size()];
            for &time in grid.mandatory_times() {
                indices[grid.index(time)?] = true;
            }
            early.exercise_indices = Some(indices);
        }

        Ok(shared(LongstaffSchwartzPathPricer::new(
            &grid,
            shared(early) as Shared<dyn EarlyExercisePathPricer<Path, State = Real>>,
            &self.process.risk_free_rate(),
        )?))
    }
}

impl<RNG: McRngTraits> MCAmericanEngine<RNG> {
    /// The C++ `controlPathPricer()` hook (`mcamericanengine.hpp:211-229`): a
    /// [`EuropeanPathPricer`] on the option type and strike, discounted from
    /// the last node of the simulation grid.
    ///
    /// # Errors
    ///
    /// Errors on a missing payoff or a negative strike; propagates a grid or
    /// discount failure.
    pub fn control_path_pricer(&self) -> QlResult<EuropeanPathPricer> {
        let Some(payoff) = &self.base.arguments().payoff else {
            fail!("no payoff given");
        };
        let grid = self.base.time_grid()?;
        let Some(last_time) = grid.back() else {
            fail!("empty time grid");
        };
        let discount = self
            .process
            .risk_free_rate()
            .current_link()?
            .discount(last_time, false)?;
        EuropeanPathPricer::new(payoff.option_type(), payoff.strike(), discount)
    }

    /// The C++ `controlVariateValue()` hook (`mcamericanengine.hpp:244-265`):
    /// an [`AnalyticEuropeanEngine`] on the same process prices the option's
    /// payoff with a European exercise on the last exercise date. The inner
    /// engine reads only the arguments and the process, no `Settings`.
    ///
    /// # Errors
    ///
    /// Errors on a missing exercise; propagates the analytic engine's failure.
    pub fn control_variate_value(&self) -> QlResult<Real> {
        let arguments = self.base.arguments();
        let Some(exercise) = &arguments.exercise else {
            fail!("no exercise given");
        };
        let mut engine = AnalyticEuropeanEngine::new(Shared::clone(&self.process));
        let Some(control_arguments) =
            (engine.arguments_mut() as &mut dyn Any).downcast_mut::<OptionArguments>()
        else {
            fail!("engine is using inconsistent arguments");
        };
        control_arguments.payoff = arguments.payoff.clone();
        control_arguments.exercise =
            Some(shared(EuropeanExercise::new(exercise.last_date())) as Shared<dyn Exercise>);
        engine.calculate()?;
        let Some(results) = (engine.results() as &dyn Any).downcast_ref::<OneAssetOptionResults>()
        else {
            fail!("engine is using inconsistent results");
        };
        let Some(value) = results.instrument.value else {
            fail!("control variation pricing engine returned no value");
        };
        Ok(value)
    }
}

impl<RNG: McRngTraits> AsObservable for MCAmericanEngine<RNG> {
    fn observable(&self) -> &Observable {
        self.base.observable()
    }
}

impl<RNG: McRngTraits> PricingEngine for MCAmericanEngine<RNG> {
    fn arguments_mut(&mut self) -> &mut dyn Arguments {
        self.base.arguments_mut()
    }

    fn results(&self) -> &dyn Results {
        self.base.results()
    }

    fn reset(&mut self) {
        self.base.reset();
    }

    /// Builds a fresh path pricer and runs both passes, then floors the value
    /// at zero under the control variate (`mcamericanengine.hpp:175-183`).
    ///
    /// # Errors
    ///
    /// Propagates a [`lsm_path_pricer`](MCAmericanEngine::lsm_path_pricer),
    /// control-variate, or simulation failure.
    fn calculate(&mut self) -> QlResult<()> {
        let pricer = self.lsm_path_pricer()?;
        let control_variate = if self.base.control_variate() {
            Some(ControlVariate {
                value: self.control_variate_value()?,
                path_pricer: Box::new(self.control_path_pricer()?),
            })
        } else {
            None
        };
        self.base.calculate_with(pricer, control_variate)?;
        if self.base.control_variate() {
            let instrument = &mut self.base.results_mut().instrument;
            instrument.value = instrument.value.map(|value| value.max(0.0));
        }
        Ok(())
    }
}

/// Factory for [`MCAmericanEngine`] (`mcamericanengine.hpp:105`), generic over
/// the RNG policy `RNG`.
///
/// As with [`MakeMcEuropeanEngine`](super::MakeMcEuropeanEngine), the validation
/// the C++ builder splits across its setters is deferred to
/// [`build`](MakeMcAmericanEngine::build) so the setters stay chainable.
pub struct MakeMcAmericanEngine<RNG> {
    process: Shared<GeneralizedBlackScholesProcess>,
    steps: Option<Size>,
    steps_per_year: Option<Size>,
    samples: Option<Size>,
    max_samples: Option<Size>,
    tolerance: Option<Real>,
    antithetic: bool,
    control_variate: bool,
    seed: u32,
    polynomial_order: Size,
    calibration_samples: Option<Size>,
    polynomial_type: PolynomialType,
    _rng: std::marker::PhantomData<RNG>,
}

impl<RNG: McRngTraits> MakeMcAmericanEngine<RNG> {
    /// Starts a builder on the given Black-Scholes process, with the C++
    /// defaults: polynomial order 2 and `Monomial` (`mcamericanengine.hpp:136`),
    /// no antithetic variate, and the driver's 2048 calibration samples.
    pub fn new(process: Shared<GeneralizedBlackScholesProcess>) -> MakeMcAmericanEngine<RNG> {
        MakeMcAmericanEngine {
            process,
            steps: None,
            steps_per_year: None,
            samples: None,
            max_samples: None,
            tolerance: None,
            antithetic: false,
            control_variate: false,
            seed: 0,
            polynomial_order: 2,
            calibration_samples: None,
            polynomial_type: PolynomialType::Monomial,
            _rng: std::marker::PhantomData,
        }
    }

    /// Sets the fixed number of time steps (`mcamericanengine.hpp:280`).
    #[must_use]
    pub fn with_steps(mut self, steps: Size) -> Self {
        self.steps = Some(steps);
        self
    }

    /// Sets the number of time steps per year (`mcamericanengine.hpp:287`).
    #[must_use]
    pub fn with_steps_per_year(mut self, steps: Size) -> Self {
        self.steps_per_year = Some(steps);
        self
    }

    /// Sets the required number of samples (`mcamericanengine.hpp:295`).
    #[must_use]
    pub fn with_samples(mut self, samples: Size) -> Self {
        self.samples = Some(samples);
        self
    }

    /// Sets the required absolute tolerance (`mcamericanengine.hpp:304`).
    #[must_use]
    pub fn with_absolute_tolerance(mut self, tolerance: Real) -> Self {
        self.tolerance = Some(tolerance);
        self
    }

    /// Sets the maximum number of samples (`mcamericanengine.hpp:317`).
    #[must_use]
    pub fn with_max_samples(mut self, samples: Size) -> Self {
        self.max_samples = Some(samples);
        self
    }

    /// Sets the RNG seed (`mcamericanengine.hpp:333`).
    #[must_use]
    pub fn with_seed(mut self, seed: u32) -> Self {
        self.seed = seed;
        self
    }

    /// Requests the antithetic-variate variance reduction
    /// (`mcamericanengine.hpp:340`), on both the pricing and, by the driver's
    /// fallback, the calibration pass.
    #[must_use]
    pub fn with_antithetic_variate(mut self, antithetic: bool) -> Self {
        self.antithetic = antithetic;
        self
    }

    /// Requests the control variate (`mcamericanengine.hpp:119,358-361`): the
    /// analytic European twin, on the pricing pass only.
    #[must_use]
    pub fn with_control_variate(mut self, control_variate: bool) -> Self {
        self.control_variate = control_variate;
        self
    }

    /// Sets the regression order (`mcamericanengine.hpp:266`).
    #[must_use]
    pub fn with_polynomial_order(mut self, order: Size) -> Self {
        self.polynomial_order = order;
        self
    }

    /// Selects the regression family. The engine rejects Legendre and
    /// first-kind Chebyshev, matching QuantLib's American path pricer.
    #[must_use]
    pub fn with_basis_system(mut self, family: PolynomialType) -> Self {
        self.polynomial_type = family;
        self
    }

    /// Sets the number of calibration paths (`mcamericanengine.hpp:325`).
    #[must_use]
    pub fn with_calibration_samples(mut self, samples: Size) -> Self {
        self.calibration_samples = Some(samples);
        self
    }

    /// Builds the configured [`MCAmericanEngine`]
    /// (`mcamericanengine.hpp:348-370`).
    ///
    /// # Errors
    ///
    /// Errors if neither or both of `steps`/`steps_per_year` are set (`:352-355`),
    /// if both `samples` and `tolerance` are set (`:296,305`), or if a tolerance
    /// is set on an RNG policy without an error estimate (`:307`).
    pub fn build(self) -> QlResult<MCAmericanEngine<RNG>> {
        require!(
            self.steps.is_some() || self.steps_per_year.is_some(),
            "number of steps not given"
        );
        require!(
            self.steps.is_none() || self.steps_per_year.is_none(),
            "number of steps overspecified"
        );
        require!(
            !(self.samples.is_some() && self.tolerance.is_some()),
            "number of samples already set"
        );
        if self.tolerance.is_some() {
            require!(
                RNG::ALLOWS_ERROR_ESTIMATE,
                "chosen random generator policy does not allow an error estimate"
            );
        }
        MCAmericanEngine::new(
            self.process,
            self.steps,
            self.steps_per_year,
            self.antithetic,
            self.control_variate,
            self.samples,
            self.tolerance,
            self.max_samples,
            self.seed,
            self.polynomial_order,
            self.polynomial_type,
            self.calibration_samples,
            None,
            None,
        )
    }
}

#[cfg(test)]
mod tests {
    use std::any::Any;

    use super::*;
    use crate::exercise::{AmericanExercise, EuropeanExercise, Exercise};
    use crate::instruments::{OptionArguments, PlainVanillaPayoff};
    use crate::math::array::Array;
    use crate::math::randomnumbers::rngtraits::PseudoRandom;
    use crate::math::timegrid::TimeGrid;
    use crate::option::OptionType;
    use crate::pricingengines::vanilla::test_market::{Market, market, time_to_days, today};
    use crate::time::date::Date;

    const STRIKE: Real = 40.0;
    const TOL: Real = 1e-14;

    fn american(expiry: Date) -> Shared<dyn Exercise> {
        shared(AmericanExercise::over(today(), expiry).unwrap()) as Shared<dyn Exercise>
    }

    fn put_pricer(order: Size) -> AmericanPathPricer {
        AmericanPathPricer::new(
            shared(PlainVanillaPayoff::new(OptionType::Put, STRIKE))
                as Shared<dyn StrikedTypePayoff>,
            order,
            PolynomialType::Monomial,
        )
    }

    fn path(values: [Real; 3]) -> Path {
        Path::new(TimeGrid::new(1.0, 2).unwrap(), Array::from(values)).unwrap()
    }

    fn flat_market() -> Market {
        let market = market();
        market.set(36.0, 0.0, 0.06, 0.20);
        market
    }

    fn engine(market: &Market) -> MCAmericanEngine<PseudoRandom> {
        MakeMcAmericanEngine::<PseudoRandom>::new(Shared::clone(&market.process))
            .with_steps(4)
            .with_samples(256)
            .with_seed(42)
            .build()
            .unwrap()
    }

    fn set_option(engine: &mut MCAmericanEngine<PseudoRandom>, exercise: Shared<dyn Exercise>) {
        let args = (engine.arguments_mut() as &mut dyn Any)
            .downcast_mut::<OptionArguments>()
            .unwrap();
        args.payoff = Some(shared(PlainVanillaPayoff::new(OptionType::Put, STRIKE))
            as Shared<dyn StrikedTypePayoff>);
        args.exercise = Some(exercise);
    }

    /// The scaling arithmetic of `mcamericanengine.cpp:48-66` on a fixture where
    /// every wrong wiring lands somewhere else: a K=40 put at a spot of 36 gives
    /// `scaling = 0.025`, `state = 0.9`, and `value = 4`. Dividing rather than
    /// multiplying in `state` gives 1440; evaluating the payoff at the SCALED
    /// state gives 39.1.
    #[test]
    fn the_state_is_scaled_and_the_value_is_not() {
        let pricer = put_pricer(3);
        let p = path([36.0, 44.0, 38.0]);

        assert!((pricer.state(&p, 0) - 0.9).abs() < TOL);
        assert!((pricer.state(&p, 1) - 1.1).abs() < TOL);
        assert!((pricer.value(&p, 0) - 4.0).abs() < TOL);
        assert_eq!(pricer.value(&p, 1), 0.0, "an OTM put is worth 0");
        assert!((pricer.value(&p, 2) - 2.0).abs() < TOL);
    }

    /// The exercise value goes through the same scaling round trip C++ takes
    /// (`mcamericanengine.cpp:58-60`), not a shortcut to `payoff(path[t])`. On a
    /// K=3 put at a spot of 0.89 the round trip is not the identity, so the two
    /// compositions differ in the last bit and the exact compare separates them.
    #[test]
    fn the_exercise_value_round_trips_through_the_scaling() {
        let pricer = AmericanPathPricer::new(
            shared(PlainVanillaPayoff::new(OptionType::Put, 3.0)) as Shared<dyn StrikedTypePayoff>,
            2,
            PolynomialType::Monomial,
        );
        let p = path([0.89, 0.89, 0.89]);

        assert_eq!(pricer.value(&p, 0), 2.1100000000000003);
        assert_ne!(pricer.value(&p, 0), 3.0 - 0.89);
    }

    /// The payoff is APPENDED to the monomials (`mcamericanengine.cpp:45-46`),
    /// so order 3 gives five functions and the last one, fed the SCALED state
    /// 0.9, must report the payoff of the unscaled 36.
    #[test]
    fn the_payoff_is_the_extra_basis_function() {
        for order in [2, 3] {
            let basis = put_pricer(order).basis_system();
            assert_eq!(
                basis.len(),
                order + 2,
                "order {order}: monomials plus payoff"
            );

            assert!((basis[0](0.9) - 1.0).abs() < TOL);
            assert!((basis[1](0.9) - 0.9).abs() < TOL);
            assert!(
                (basis[order + 1](0.9) - 4.0).abs() < TOL,
                "the appended function must unscale before applying the payoff"
            );
            assert_eq!(
                basis[order + 1](1.1),
                0.0,
                "and must stay a payoff, not a monomial"
            );
        }
    }

    /// The exercise guards of `mcamericanengine.hpp:196-198`: a plain American
    /// exercise is accepted, a European one and an American one paying at
    /// expiry are not.
    #[test]
    fn only_a_plain_american_exercise_builds_a_path_pricer() {
        let market = flat_market();
        let expiry = today() + time_to_days(1.0);

        let mut accepted = engine(&market);
        set_option(&mut accepted, american(expiry));
        assert!(accepted.lsm_path_pricer().is_ok());

        let mut rejected = engine(&market);
        set_option(
            &mut rejected,
            shared(EuropeanExercise::new(expiry)) as Shared<dyn Exercise>,
        );
        assert_eq!(
            rejected.lsm_path_pricer().err().unwrap().message(),
            "wrong exercise given"
        );

        let mut at_expiry = engine(&market);
        set_option(
            &mut at_expiry,
            shared(AmericanExercise::new(today(), expiry, true).unwrap()) as Shared<dyn Exercise>,
        );
        assert_eq!(
            at_expiry.lsm_path_pricer().err().unwrap().message(),
            "payoff at expiry not handled"
        );
    }

    /// An engine with nothing set reports the missing exercise before anything
    /// else touches it.
    #[test]
    fn a_missing_exercise_is_rejected() {
        let market = flat_market();
        let mut bare = engine(&market);
        assert_eq!(
            bare.lsm_path_pricer().err().unwrap().message(),
            "no exercise given"
        );

        let args = (bare.arguments_mut() as &mut dyn Any)
            .downcast_mut::<OptionArguments>()
            .unwrap();
        args.exercise = Some(american(today() + time_to_days(1.0)));
        assert_eq!(
            bare.lsm_path_pricer().err().unwrap().message(),
            "no payoff given"
        );
    }

    /// The builder defaults of `mcamericanengine.hpp:130-137`: order 2, no
    /// antithetic variate, and the driver's 2048 calibration samples.
    #[test]
    fn the_builder_defaults_match_the_cpp_factory() {
        let market = flat_market();
        let built = engine(&market);
        assert_eq!(built.polynomial_order(), 2);
        assert_eq!(built.lsm_base().n_calibration_samples(), 2048);
        assert!(!built.lsm_base().antithetic_variate_calibration());

        let overridden = MakeMcAmericanEngine::<PseudoRandom>::new(Shared::clone(&market.process))
            .with_steps(4)
            .with_samples(256)
            .with_polynomial_order(4)
            .with_calibration_samples(64)
            .build()
            .unwrap();
        assert_eq!(overridden.polynomial_order(), 4);
        assert_eq!(overridden.lsm_base().n_calibration_samples(), 64);
    }

    /// The build guards of `mcamericanengine.hpp:296,305,352-355`.
    #[test]
    fn the_builder_validates_its_named_parameters() {
        let market = flat_market();
        let maker = || MakeMcAmericanEngine::<PseudoRandom>::new(Shared::clone(&market.process));

        assert!(maker().with_samples(256).build().is_err(), "no steps given");
        assert!(
            maker()
                .with_steps(4)
                .with_steps_per_year(50)
                .with_samples(256)
                .build()
                .is_err(),
            "steps overspecified"
        );
        assert!(
            maker()
                .with_steps(4)
                .with_samples(256)
                .with_absolute_tolerance(0.02)
                .build()
                .is_err(),
            "samples and tolerance are exclusive"
        );
        let antithetic = maker()
            .with_steps(4)
            .with_samples(256)
            .with_antithetic_variate(true)
            .build()
            .unwrap();
        assert!(
            antithetic.lsm_base().antithetic_variate_calibration(),
            "the pricing flag must reach the engine, not a hardcoded false"
        );
        assert!(
            maker()
                .with_steps(4)
                .with_absolute_tolerance(0.02)
                .with_max_samples(4_096)
                .build()
                .is_ok()
        );
    }

    #[test]
    fn bermudan_grid_retains_only_positive_mandatory_dates() {
        use crate::exercise::BermudanExercise;
        let market = flat_market();
        let mut engine = engine(&market);
        set_option(
            &mut engine,
            shared(
                BermudanExercise::new(
                    vec![
                        today() - 3,
                        today(),
                        today() + 91,
                        today() + 91,
                        today() + 203,
                        today() + 365,
                    ],
                    false,
                )
                .unwrap(),
            ),
        );
        let grid = engine.lsm_base().time_grid().unwrap();
        assert_eq!(
            grid.mandatory_times(),
            &[91.0 / 360.0, 203.0 / 360.0, 365.0 / 360.0]
        );
        assert_eq!(grid.size(), 5);
        assert_eq!(grid[1], 91.0 / 360.0);
        assert_eq!(grid[2], 203.0 / 360.0);
        assert!(engine.lsm_path_pricer().is_ok());
        set_option(
            &mut engine,
            shared(BermudanExercise::new(vec![today()], false).unwrap()),
        );
        assert!(
            engine
                .lsm_path_pricer()
                .err()
                .unwrap()
                .message()
                .contains("no positive exercise time")
        );
        set_option(
            &mut engine,
            shared(BermudanExercise::new(vec![today() + 365], true).unwrap()),
        );
        assert_eq!(
            engine.lsm_path_pricer().err().unwrap().message(),
            "payoff at expiry not handled"
        );
    }

    #[test]
    fn bermudan_mask_forbids_exercise_between_contract_dates_in_both_passes() {
        use crate::methods::montecarlo::PathPricer;
        let market = flat_market();
        let grid = TimeGrid::new(1.0, 2).unwrap();
        for (allowed, expected_positive) in [(false, false), (true, true)] {
            let mut early = put_pricer(2);
            early.exercise_indices = Some(vec![false, allowed, true]);
            let lsm = LongstaffSchwartzPathPricer::new(
                &grid,
                shared(early),
                &market.process.risk_free_rate(),
            )
            .unwrap();
            let sample = path([40.0, 1.0, 40.0]);
            assert_eq!(lsm.price(&sample), 0.0);
            lsm.calibrate().unwrap();
            assert_eq!(lsm.price(&sample) > 0.0, expected_positive);
            assert_eq!(
                lsm.exercise_probability().unwrap(),
                if allowed { 1.0 } else { 0.0 }
            );
        }
    }

    #[test]
    fn unsupported_engine_bases_are_rejected_before_sampling() {
        let market = flat_market();
        for family in [PolynomialType::Legendre, PolynomialType::Chebyshev] {
            let error = MakeMcAmericanEngine::<PseudoRandom>::new(Shared::clone(&market.process))
                .with_steps(4)
                .with_samples(16)
                .with_basis_system(family)
                .build()
                .err()
                .unwrap();
            assert_eq!(error.message(), "insufficient polynomial type");
        }
    }
}

#[cfg(test)]
mod oracle {
    //! The American-MC milestone: `test-suite/mclongstaffschwartzengine.cpp:123`
    //! `testAmericanOption`, the `i = 0, j = 0` case.
    //!
    //! Fixture, digit for digit from the C++ (`:127-193`): an American put on a
    //! spot of 36 struck at 36, `q = 0`, `r = 6%`, `sigma = 20%`, evaluation
    //! date 15 May 1998, curve reference 17 May 1998, maturity 17 May 1999,
    //! Actual365Fixed throughout. The engine is
    //! `MakeMCAmericanEngine<PseudoRandom>` with 75 steps, the antithetic
    //! variate, an absolute tolerance of 0.02, seed 42, polynomial order 3 over
    //! the Monomial basis, and the driver's default 2048 calibration paths. The
    //! evaluation date is deliberately NOT the curves' reference date; the C++
    //! fixture is the same way round.
    //!
    //! REFERENCE SUBSTITUTION, stated plainly. The C++ test reprices the option
    //! with `FdBlackScholesVanillaEngine(process, 401, 200)` and checks
    //! `|mc - fd| < 2.34 * errorEstimate` (`:201-206`). This historical test
    //! predates this crate's American FD support and retains its cached MC
    //! reference. The reference is the MC value QuantLib itself produces on this
    //! fixture, measured on a locally built QuantLib 1.43 dylib:
    //! `mc = 2.054422273006143`, `errorEstimate = 0.01775722870215829`,
    //! `exerciseProbability = 0.4897360703812317`, `fd = 2.08679820123328`.
    //! The band factor 2.34 is the C++ one unchanged.
    //!
    //! The 2.105 that the C++ file records in a comment (`:154`) is NOT usable
    //! as the reference: it is a third-party binomial number that fails the C++
    //! test's own band against QuantLib's own MC value
    //! (`|2.0544 - 2.105| = 0.0506 > 0.0416`), and an independent
    //! Cox-Rubinstein tree at 20001 steps puts the true American price at
    //! 2.08764, agreeing with the FD engine rather than with 2.105.
    //!
    //! Rust and C++ do not share a sample path bit for bit: the generated paths
    //! agree to 14 significant digits (a 75-step accumulation of last-bit
    //! ordering differences), and the near-collinear order-3 regression
    //! amplifies that into a different exercise boundary at only 2048
    //! calibration paths. The two agree where that noise washes out: at 131072
    //! calibration paths Rust prices 2.06774 against C++'s 2.06907, 0.07 error
    //! estimates apart, with exercise probabilities 0.4703 and 0.4712.
    //!
    //! Three independent gates: the price against QuantLib's own value within
    //! the C++ band, the exercise probability against 0.48013 within the C++
    //! 1.5% tolerance (`:154,214`), and the never-early-exercise floor, since
    //! an American put cannot be worth less than its European twin.
    //!
    //! The five remaining parameter cases below use independently generated
    //! QuantLib FD references and the original band/probability tolerances.
    //! The first-case cached-MC exception above remains explicit and unchanged.
    //! The Brownian bridge is not separate work: C++ fixes it to `false`
    //! (`mcamericanengine.hpp:161,169`). Multi-asset LSM remains separate
    //! work; the control-variate oracles close this module.

    use std::any::Any;

    use super::{MCAmericanEngine, MakeMcAmericanEngine};
    use crate::exercise::{AmericanExercise, EuropeanExercise, Exercise};
    use crate::handle::Handle;
    use crate::instrument::Instrument;
    use crate::instruments::{OneAssetOptionResults, OptionArguments};
    use crate::instruments::{PlainVanillaPayoff, StrikedTypePayoff, VanillaOption};
    use crate::interestrate::Compounding;
    use crate::math::randomnumbers::rngtraits::McRngTraits;
    use crate::math::randomnumbers::rngtraits::PseudoRandom;
    use crate::math::statistics::{GeneralStatistics, MeanStdDev, Statistics};
    use crate::methods::montecarlo::{MonteCarloModel, PathGenerator};
    use crate::option::OptionType;
    use crate::pricingengine::PricingEngine;
    use crate::pricingengines::vanilla::AnalyticEuropeanEngine;
    use crate::processes::GeneralizedBlackScholesProcess;
    use crate::quotes::{Quote, SimpleQuote};
    use crate::settings::Settings;
    use crate::shared::{Shared, SharedMut, shared, shared_mut};
    use crate::stochasticprocess::StochasticProcess1D;
    use crate::termstructures::volatility::{BlackConstantVol, BlackVolTermStructure};
    use crate::termstructures::yields::FlatForward;
    use crate::termstructures::yieldtermstructure::YieldTermStructure;
    use crate::time::date::{Date, Month};
    use crate::time::daycounters::actual365fixed::Actual365Fixed;
    use crate::time::frequency::Frequency;
    use crate::types::Size;
    use crate::types::{Rate, Real, Volatility};

    const UNDERLYING: Real = 36.0;
    const DIVIDEND_YIELD: Rate = 0.0;
    const RISK_FREE_RATE: Rate = 0.06;
    const VOLATILITY: Volatility = 0.20;

    const QUANTLIB_MC_VALUE: Real = 2.054422273006143;
    const EXPECTED_EXERCISE_PROBABILITY: Real = 0.48013;

    fn todays_date() -> Date {
        Date::new(15, Month::May, 1998)
    }

    fn settlement_date() -> Date {
        Date::new(17, Month::May, 1998)
    }

    fn maturity() -> Date {
        Date::new(17, Month::May, 1999)
    }

    fn flat_curve(rate: Rate) -> Handle<dyn YieldTermStructure> {
        Handle::new(shared(FlatForward::with_rate(
            settlement_date(),
            rate,
            Actual365Fixed::new(),
            Compounding::Continuous,
            Frequency::Annual,
        )) as Shared<dyn YieldTermStructure>)
    }

    fn process() -> Shared<GeneralizedBlackScholesProcess> {
        process_with_vol(VOLATILITY)
    }

    fn process_with_vol(volatility: Real) -> Shared<GeneralizedBlackScholesProcess> {
        let spot = Handle::new(shared(SimpleQuote::new(UNDERLYING)) as Shared<dyn Quote>);
        let vol = Handle::new(shared(BlackConstantVol::new(
            settlement_date(),
            None,
            volatility,
            Actual365Fixed::new(),
        )) as Shared<dyn BlackVolTermStructure>);
        shared(GeneralizedBlackScholesProcess::new(
            spot,
            flat_curve(DIVIDEND_YIELD),
            flat_curve(RISK_FREE_RATE),
            vol,
        ))
    }

    fn payoff() -> Shared<dyn StrikedTypePayoff> {
        shared(PlainVanillaPayoff::new(OptionType::Put, UNDERLYING))
            as Shared<dyn StrikedTypePayoff>
    }

    #[test]
    fn american_put_reproduces_the_quantlib_price_and_exercise_probability() {
        let settings = shared(Settings::new());
        settings.set_evaluation_date(todays_date());
        let process = process();

        let exercise = shared(AmericanExercise::over(settlement_date(), maturity()).unwrap())
            as Shared<dyn Exercise>;
        let mut american = VanillaOption::new(payoff(), exercise, Shared::clone(&settings));
        american.base_mut().set_pricing_engine(shared_mut(
            MakeMcAmericanEngine::<PseudoRandom>::new(Shared::clone(&process))
                .with_steps(75)
                .with_antithetic_variate(true)
                .with_absolute_tolerance(0.02)
                .with_seed(42)
                .with_polynomial_order(3)
                .build()
                .unwrap(),
        ) as SharedMut<dyn PricingEngine>);

        let calculated = american.npv().unwrap();
        let error_estimate = american.error_estimate().unwrap();
        let exercise_probability = american.result::<Real>("exerciseProbability").unwrap();

        let mut european = VanillaOption::new(
            payoff(),
            shared(EuropeanExercise::new(maturity())) as Shared<dyn Exercise>,
            settings,
        );
        european.base_mut().set_pricing_engine(
            shared_mut(AnalyticEuropeanEngine::new(process)) as SharedMut<dyn PricingEngine>
        );
        let european_value = european.npv().unwrap();

        assert!(
            (calculated - QUANTLIB_MC_VALUE).abs() < 2.34 * error_estimate,
            "price {calculated} +/- {error_estimate} misses QuantLib's \
             {QUANTLIB_MC_VALUE} by {}, band {}",
            (calculated - QUANTLIB_MC_VALUE).abs(),
            2.34 * error_estimate
        );
        assert!(
            (exercise_probability - EXPECTED_EXERCISE_PROBABILITY).abs() < 0.015,
            "exercise probability {exercise_probability} vs \
             {EXPECTED_EXERCISE_PROBABILITY}"
        );
        assert!(
            calculated > european_value,
            "an American put {calculated} cannot be worth less than its \
             European twin {european_value}"
        );
    }

    #[test]
    fn five_remaining_american_cases_preserve_upstream_acceptance() {
        let references = [
            (36.0, 0.2 + 0.1, 3.430219464343261, 0.51678),
            (36.0, 0.4, 4.785433883245219, 0.54598),
            (40.0, 0.2, 4.485350467454564, 0.75549),
            (40.0, 0.2 + 0.1, 5.736716960463202, 0.67569),
            (40.0, 0.4, 7.107644070425648, 0.65562),
        ];
        for (strike, volatility, fd, probability) in references {
            let settings = shared(Settings::new());
            settings.set_evaluation_date(todays_date());
            let process = process_with_vol(volatility);
            let exercise = shared(AmericanExercise::until(maturity(), false).unwrap());
            let mut option = VanillaOption::new(
                shared(PlainVanillaPayoff::new(OptionType::Put, strike)),
                exercise,
                settings,
            );
            option.base_mut().set_pricing_engine(shared_mut(
                MakeMcAmericanEngine::<PseudoRandom>::new(process)
                    .with_steps(75)
                    .with_antithetic_variate(true)
                    .with_absolute_tolerance(0.02)
                    .with_seed(42)
                    .with_polynomial_order(3)
                    .build()
                    .unwrap(),
            ));
            let value = option.npv().unwrap();
            let error = option.error_estimate().unwrap();
            assert!(
                error.is_finite() && error > 0.0,
                "invalid standard error {error}"
            );
            let exercise = option.result::<Real>("exerciseProbability").unwrap();
            assert!(
                (value - fd).abs() <= 2.34 * error,
                "strike={strike}, vol={volatility}: {value} +/- {error} vs FD {fd}"
            );
            assert!(
                (exercise - probability).abs() <= 0.015,
                "strike={strike}, vol={volatility}: exercise {exercise} vs {probability}"
            );
        }
    }

    #[test]
    fn bermudan_exercise_only_and_refined_grids_match_independent_oracles() {
        use crate::exercise::BermudanExercise;
        for (steps, expected) in [(3, 4.331587683099873), (75, 4.334758948830429)] {
            let settings = shared(Settings::new());
            settings.set_evaluation_date(todays_date());
            let exercise = shared(
                BermudanExercise::new(
                    vec![settlement_date() + 91, settlement_date() + 203, maturity()],
                    false,
                )
                .unwrap(),
            );
            let mut option = VanillaOption::new(
                shared(PlainVanillaPayoff::new(OptionType::Put, 40.0)),
                exercise,
                settings,
            );
            option.base_mut().set_pricing_engine(shared_mut(
                MakeMcAmericanEngine::<PseudoRandom>::new(process())
                    .with_steps(steps)
                    .with_samples(32768)
                    .with_calibration_samples(8192)
                    .with_seed(42)
                    .with_antithetic_variate(true)
                    .build()
                    .unwrap(),
            ));
            let value = option.npv().unwrap();
            let error = option.error_estimate().unwrap();
            assert!(
                error.is_finite() && error > 0.0,
                "invalid standard error {error}"
            );
            assert!(
                (value - expected).abs() <= 2.34 * error,
                "steps={steps}: {value} +/- {error} vs {expected}"
            );
        }
    }

    const CV_SAMPLES: Size = 4096;

    fn cv_engine(
        strike: Real,
        control_variate: bool,
        samples: Size,
        seed: u32,
    ) -> MCAmericanEngine<PseudoRandom> {
        cv_engine_with(strike, true, control_variate, samples, seed)
    }

    fn cv_engine_with(
        strike: Real,
        antithetic_variate: bool,
        control_variate: bool,
        samples: Size,
        seed: u32,
    ) -> MCAmericanEngine<PseudoRandom> {
        let mut engine = MakeMcAmericanEngine::<PseudoRandom>::new(process())
            .with_steps(75)
            .with_antithetic_variate(antithetic_variate)
            .with_control_variate(control_variate)
            .with_samples(samples)
            .with_seed(seed)
            .with_polynomial_order(3)
            .build()
            .unwrap();
        let args = (engine.arguments_mut() as &mut dyn Any)
            .downcast_mut::<OptionArguments>()
            .unwrap();
        args.payoff = Some(shared(PlainVanillaPayoff::new(OptionType::Put, strike))
            as Shared<dyn StrikedTypePayoff>);
        args.exercise = Some(
            shared(AmericanExercise::over(settlement_date(), maturity()).unwrap())
                as Shared<dyn Exercise>,
        );
        engine.calculate().unwrap();
        engine
    }

    /// The value, error estimate, and exercise probability of a calculation.
    fn outcome(engine: &MCAmericanEngine<PseudoRandom>) -> (Real, Real, Real) {
        let results = (engine.results() as &dyn Any)
            .downcast_ref::<OneAssetOptionResults>()
            .unwrap();
        let probability = *results.instrument.additional_results["exerciseProbability"]
            .downcast_ref::<Real>()
            .unwrap();
        (
            results.instrument.value.unwrap(),
            results.instrument.error_estimate.unwrap(),
            probability,
        )
    }

    /// The mean and error of the engine's own control pricer over the pricing
    /// paths, rebuilt independently: same grid, same seed, same antithetic
    /// pairing.
    fn european_over_the_pricing_paths(
        engine: &MCAmericanEngine<PseudoRandom>,
        samples: Size,
        seed: u32,
    ) -> (Real, Real) {
        let grid = engine.lsm_base().time_grid().unwrap();
        let generator = PseudoRandom::make_sequence_generator(grid.size() - 1, seed).unwrap();
        let paths = PathGenerator::from_time_grid(
            process() as Shared<dyn StochasticProcess1D>,
            grid,
            generator,
            false,
        )
        .unwrap();
        let mut model = MonteCarloModel::new(
            paths,
            engine.control_path_pricer().unwrap(),
            GeneralStatistics::new(),
            true,
        )
        .unwrap();
        model.add_samples(samples).unwrap();
        let accumulator = model.sample_accumulator();
        (
            accumulator.mean().unwrap(),
            accumulator.error_estimate().unwrap(),
        )
    }

    /// The CV oracles on the `mclongstaffschwartzengine.cpp:123` fixture, at
    /// a fixed sample count so both runs draw the SAME pricing paths. No QL
    /// test constructs `MCAmericanEngine` with a control variate, so the
    /// oracles are the deterministic consequences of the formula
    /// (`montecarlomodel.hpp:98-117`) rather than a cached number:
    /// - the CV run minus the plain run is exactly `analytic - mean(european)`
    ///   over those paths (the shift is material, so skipping the adjustment
    ///   fails);
    /// - the exercise probability is bit-identical, since the control never
    ///   reaches the Longstaff-Schwartz pricer (`mclongstaffschwartzengine.hpp:204`);
    /// - the control value is the analytic European twin and the control
    ///   pricer is an unbiased estimator of it.
    ///
    /// No FD band is asserted: a control variate does not remove the LSM low
    /// bias, so a smaller error would fail a band the plain run only just meets.
    #[test]
    fn control_variate_shifts_by_the_european_error_on_the_same_paths() {
        const SEED: u32 = 42;
        let plain = cv_engine(UNDERLYING, false, CV_SAMPLES, SEED);
        let controlled = cv_engine(UNDERLYING, true, CV_SAMPLES, SEED);
        let (v0, e0, p0) = outcome(&plain);
        let (v1, e1, p1) = outcome(&controlled);
        let analytic = controlled.control_variate_value().unwrap();
        let (mean, mean_error) = european_over_the_pricing_paths(&controlled, CV_SAMPLES, SEED);

        assert!(
            ((v1 - v0) - (analytic - mean)).abs() < 1e-12,
            "cv {v1} - plain {v0} != analytic {analytic} - european mean {mean}"
        );
        assert!((analytic - mean).abs() > 1e-4, "the shift must be material");
        assert_eq!(p1, p0, "the control must not touch the exercise decision");
        assert!(e0.is_finite() && e1.is_finite() && e1 > 0.0);

        let settings = shared(Settings::new());
        settings.set_evaluation_date(todays_date());
        let mut european = VanillaOption::new(
            payoff(),
            shared(EuropeanExercise::new(maturity())) as Shared<dyn Exercise>,
            settings,
        );
        european.base_mut().set_pricing_engine(
            shared_mut(AnalyticEuropeanEngine::new(process())) as SharedMut<dyn PricingEngine>
        );
        assert_eq!(analytic, european.npv().unwrap());
        assert!(
            (mean - analytic).abs() < 4.0 * mean_error,
            "control pricer mean {mean} +/- {mean_error} vs analytic {analytic}"
        );
    }

    /// The error estimate shrinks where the European twin tracks the American
    /// value. QuantLib's control enters with a fixed coefficient of one
    /// (`montecarlomodel.hpp:100`), so it reduces the variance only when
    /// `2 cov(american, european) > var(european)`, that is when the optimal
    /// coefficient `beta*` exceeds one half. Two pins on the same fixture:
    /// - the antithetic out-of-the-money K=32 put: 0.01184 against 0.01380;
    /// - the NON-antithetic at-the-money K=36 put: 0.03257 against 0.03817
    ///   (`beta* = 0.59`).
    ///
    /// The at-the-money failure needs the antithetic variate as well: with it,
    /// K=36 gives 0.02278 against 0.01662 under the same exercise probability.
    /// Antithetic pairing cuts `var(american)` sharply but leaves the residual
    /// `american - european`, which is almost even in the Gaussian draw,
    /// untouched; the review's probe on its own calibration seed measures se
    /// 0.0278 to 0.0174 for the former and 0.02198 single against 0.02191
    /// paired for the latter (`docs/internal/reviews-2026-11-08/1363.md`).
    /// After that cut the fixed coefficient overshoots: `beta*` falls to 0.32
    /// on this engine's calibration (0.37 in the review's probe).
    #[test]
    fn control_variate_reduces_the_error_where_the_twin_tracks_the_value() {
        for (strike, antithetic) in [(32.0, true), (UNDERLYING, false)] {
            let (_, plain, _) = outcome(&cv_engine_with(strike, antithetic, false, CV_SAMPLES, 42));
            let (_, controlled, _) =
                outcome(&cv_engine_with(strike, antithetic, true, CV_SAMPLES, 42));
            assert!(
                controlled < plain,
                "K={strike}, antithetic={antithetic}: cv error {controlled} \
                 must fall below plain error {plain}"
            );
        }
    }

    /// The `max(0, value)` floor under the control variate
    /// (`mcamericanengine.hpp:178-181`). On this deep-OTM put and seed, found
    /// by scanning, the unfloored CV estimate `plain + analytic - mean` is
    /// about `-0.029`; the engine must report exactly zero.
    #[test]
    fn a_negative_control_variate_estimate_is_floored_at_zero() {
        const STRIKE: Real = 22.0;
        const SAMPLES: Size = 64;
        const SEED: u32 = 16;
        let plain = cv_engine(STRIKE, false, SAMPLES, SEED);
        let controlled = cv_engine(STRIKE, true, SAMPLES, SEED);
        let analytic = controlled.control_variate_value().unwrap();
        let (mean, _) = european_over_the_pricing_paths(&controlled, SAMPLES, SEED);
        let raw = outcome(&plain).0 + analytic - mean;

        assert!(
            raw < -0.01,
            "fixture must produce a negative raw estimate: {raw}"
        );
        assert_eq!(outcome(&controlled).0, 0.0);
    }
}