ferro_ta_core 1.1.0

//! Option Greeks.

use super::normal::{cdf, pdf};
use super::pricing::{black_76_price, black_scholes_price};
use super::{Greeks, OptionEvaluation, OptionKind, PricingModel};

fn bs_inputs_valid(
    underlying: f64,
    strike: f64,
    rate: f64,
    carry: f64,
    time_to_expiry: f64,
    volatility: f64,
) -> bool {
    underlying.is_finite()
        && strike.is_finite()
        && rate.is_finite()
        && carry.is_finite()
        && time_to_expiry.is_finite()
        && volatility.is_finite()
        && underlying > 0.0
        && strike > 0.0
        && time_to_expiry > 0.0
        && volatility > 0.0
}

fn numerical_theta<F>(time_to_expiry: f64, price_fn: F) -> f64
where
    F: Fn(f64) -> f64,
{
    if time_to_expiry <= 0.0 {
        return 0.0;
    }
    let h = time_to_expiry.clamp(1e-6, 1.0 / 365.0);
    let t_minus = (time_to_expiry - h).max(1e-8);
    let t_plus = time_to_expiry + h;
    let price_minus = price_fn(t_minus);
    let price_plus = price_fn(t_plus);
    (price_minus - price_plus) / (t_plus - t_minus)
}

/// Black-Scholes-Merton Greeks.
pub fn black_scholes_greeks(
    spot: f64,
    strike: f64,
    rate: f64,
    dividend_yield: f64,
    time_to_expiry: f64,
    volatility: f64,
    kind: OptionKind,
) -> Greeks {
    if !bs_inputs_valid(
        spot,
        strike,
        rate,
        dividend_yield,
        time_to_expiry,
        volatility,
    ) {
        return Greeks {
            delta: f64::NAN,
            gamma: f64::NAN,
            vega: f64::NAN,
            theta: f64::NAN,
            rho: f64::NAN,
        };
    }

    let sqrt_t = time_to_expiry.sqrt();
    let sigma_sqrt_t = volatility * sqrt_t;
    let discount = (-rate * time_to_expiry).exp();
    let carry_discount = (-dividend_yield * time_to_expiry).exp();
    let d1 = ((spot / strike).ln()
        + (rate - dividend_yield + 0.5 * volatility * volatility) * time_to_expiry)
        / sigma_sqrt_t;
    let d2 = d1 - sigma_sqrt_t;
    let pdf_d1 = pdf(d1);

    let delta = match kind {
        OptionKind::Call => carry_discount * cdf(d1),
        OptionKind::Put => carry_discount * (cdf(d1) - 1.0),
    };
    let gamma = carry_discount * pdf_d1 / (spot * sigma_sqrt_t);
    let vega = spot * carry_discount * pdf_d1 * sqrt_t;
    let theta = match kind {
        OptionKind::Call => {
            -(spot * carry_discount * pdf_d1 * volatility) / (2.0 * sqrt_t)
                - rate * strike * discount * cdf(d2)
                + dividend_yield * spot * carry_discount * cdf(d1)
        }
        OptionKind::Put => {
            -(spot * carry_discount * pdf_d1 * volatility) / (2.0 * sqrt_t)
                + rate * strike * discount * cdf(-d2)
                - dividend_yield * spot * carry_discount * cdf(-d1)
        }
    };
    let rho = match kind {
        OptionKind::Call => strike * time_to_expiry * discount * cdf(d2),
        OptionKind::Put => -strike * time_to_expiry * discount * cdf(-d2),
    };

    Greeks {
        delta,
        gamma,
        vega,
        theta,
        rho,
    }
}

/// Black-76 Greeks with respect to the forward.
pub fn black_76_greeks(
    forward: f64,
    strike: f64,
    rate: f64,
    time_to_expiry: f64,
    volatility: f64,
    kind: OptionKind,
) -> Greeks {
    if !bs_inputs_valid(forward, strike, rate, 0.0, time_to_expiry, volatility) {
        return Greeks {
            delta: f64::NAN,
            gamma: f64::NAN,
            vega: f64::NAN,
            theta: f64::NAN,
            rho: f64::NAN,
        };
    }

    let sqrt_t = time_to_expiry.sqrt();
    let sigma_sqrt_t = volatility * sqrt_t;
    let discount = (-rate * time_to_expiry).exp();
    let d1 =
        ((forward / strike).ln() + 0.5 * volatility * volatility * time_to_expiry) / sigma_sqrt_t;
    let pdf_d1 = pdf(d1);

    let delta = match kind {
        OptionKind::Call => discount * cdf(d1),
        OptionKind::Put => -discount * cdf(-d1),
    };
    let gamma = discount * pdf_d1 / (forward * sigma_sqrt_t);
    let vega = discount * forward * pdf_d1 * sqrt_t;
    let theta = numerical_theta(time_to_expiry, |t| {
        black_76_price(forward, strike, rate, t, volatility, kind)
    });
    let rho =
        -time_to_expiry * black_76_price(forward, strike, rate, time_to_expiry, volatility, kind);

    Greeks {
        delta,
        gamma,
        vega,
        theta,
        rho,
    }
}

/// Model-dispatched Greeks.
pub fn model_greeks(input: OptionEvaluation) -> Greeks {
    let contract = input.contract;
    match contract.model {
        PricingModel::BlackScholes => black_scholes_greeks(
            contract.underlying,
            contract.strike,
            contract.rate,
            contract.carry,
            contract.time_to_expiry,
            input.volatility,
            contract.kind,
        ),
        PricingModel::Black76 => black_76_greeks(
            contract.underlying,
            contract.strike,
            contract.rate,
            contract.time_to_expiry,
            input.volatility,
            contract.kind,
        ),
    }
}

/// Price derivative with respect to calendar time using the selected model.
pub fn model_theta(input: OptionEvaluation) -> f64 {
    let contract = input.contract;
    numerical_theta(contract.time_to_expiry, |t| match contract.model {
        PricingModel::BlackScholes => black_scholes_price(
            contract.underlying,
            contract.strike,
            contract.rate,
            contract.carry,
            t,
            input.volatility,
            contract.kind,
        ),
        PricingModel::Black76 => black_76_price(
            contract.underlying,
            contract.strike,
            contract.rate,
            t,
            input.volatility,
            contract.kind,
        ),
    })
}

#[cfg(test)]
mod tests {
    use super::{black_76_greeks, black_scholes_greeks};
    use crate::options::OptionKind;

    #[test]
    fn bsm_greeks_are_finite() {
        let g = black_scholes_greeks(100.0, 100.0, 0.05, 0.0, 1.0, 0.2, OptionKind::Call);
        assert!(g.delta.is_finite());
        assert!(g.gamma.is_finite());
        assert!(g.vega.is_finite());
        assert!(g.theta.is_finite());
        assert!(g.rho.is_finite());
    }

    #[test]
    fn black_76_greeks_are_finite() {
        let g = black_76_greeks(100.0, 100.0, 0.03, 1.0, 0.2, OptionKind::Put);
        assert!(g.delta.is_finite());
        assert!(g.gamma.is_finite());
        assert!(g.vega.is_finite());
        assert!(g.theta.is_finite());
        assert!(g.rho.is_finite());
    }
}