SABR

use helixrs::{
    RateVolSurface, SabrFormula, SabrParams, SabrSpec, VolConvention, alpha_from_atm,
    calibrate_sabr, sabr_vol,
};

type Outcome<T> = Result<T, Box<dyn std::error::Error>>;

const FORWARD: f64 = 0.045;
const ATM: f64 = 0.0100;
const EXPIRY: f64 = 1.0;
const BETA: f64 = 0.5;
const RHO: f64 = -0.2;
const NU: f64 = 0.35;
const SPREADS: [f64; 7] = [-0.02, -0.01, -0.005, 0.0, 0.005, 0.01, 0.02];

fn main() -> Outcome<()> {
    let formula = SabrFormula::HaganNormal;

    // α from the ATM vol, then the normal-vol smile across strikes around the
    // forward.
    let alpha = alpha_from_atm(formula, FORWARD, ATM, EXPIRY, BETA, RHO, NU, 0.0)?;
    let params = SabrParams { alpha, beta: BETA, rho: RHO, nu: NU, shift: 0.0 };
    let mut smile = Vec::new();
    for spread in SPREADS {
        let vol = sabr_vol(formula, FORWARD, FORWARD + spread, EXPIRY, &params)?;
        println!("strike {:.4}  normal vol {vol:.6}", FORWARD + spread);
        smile.push(vol);
    }

    // The smile as a quoted cube — one expiry, one tenor, strikes as spreads to the
    // forward — fitted under the same formula and β. ρ and ν come back.
    let cube = RateVolSurface::cube(vec![EXPIRY], vec![5.0], SPREADS.to_vec(), &[vec![smile.clone()]], VolConvention::Normal)?
        .over_the_forward();
    let spec = SabrSpec::new(formula, BETA, 0.0)?.with_accept(2e-3).with_max_restarts(20);
    println!(
        "beta {:.2}  shift {:.4}  accept {:.3}  restarts {}",
        spec.beta, spec.shift, spec.accept, spec.max_restarts
    );
    let fit = calibrate_sabr(&cube, &[vec![FORWARD]], &spec)?;
    let slice = &fit.slices[0];
    println!("rho {:.10}  nu {:.10}", slice.rho, slice.nu);

    Ok(())
}

import helixio as hlx

vols = hlx.vols
FORWARD, ATM, EXPIRY, BETA, RHO, NU = 0.045, 0.0100, 1.0, 0.5, -0.2, 0.35
SPREADS = [-0.02, -0.01, -0.005, 0.0, 0.005, 0.01, 0.02]

# α from the ATM vol, then the normal-vol smile across strikes around the
# forward.
alpha = vols.alpha_from_atm("HaganNormal", FORWARD, ATM, EXPIRY, BETA, RHO, NU)
smile = [vols.sabr_vol("HaganNormal", FORWARD, FORWARD + s, EXPIRY, alpha, BETA, RHO, NU) for s in SPREADS]
for spread, vol in zip(SPREADS, smile):
    print(f"strike {FORWARD + spread:.4f}  normal vol {vol:.6f}")

# The smile as a quoted cube — one expiry, one tenor, strikes as spreads to the
# forward — fitted under the same formula and β. ρ and ν come back.
cube = vols.RateVolSurface.cube([EXPIRY], [5.0], SPREADS, [[smile]], vol_convention="normal", strike_axis="spread_to_atm")
spec = vols.SabrSpec("HaganNormal", BETA, 0.0)
print(f"beta {spec.beta:.2f}  shift {spec.shift:.4f}  accept {spec.accept:.3f}  restarts {spec.max_restarts}")
fit = vols.calibrate_sabr(cube, [[FORWARD]], spec)
slice_ = {name: column[0] for name, column in fit.diagnostics().to_dict().items()}
print(f"rho {slice_['rho']:.10f}  nu {slice_['nu']:.10f}")