Calibration generates negative values

[eliebnn]

Hi,

I have tried to run the calibration code. Some runs return negative values for v0, theta, kappa, signa, which should all be strictly positive.

Attached is a code sample. It runs the calibration over several v0, and keep the minimul mape loss.

Also, if you uncomment the set_initial_params line, you will see that sigma and rho will have NaN assigned values.

Am I doing something wrong? I run the calibration over call options with 1 months maturity with same spot, and different strikes.

use stochastic_rs::quant::calibration::heston::{HestonCalibrator, HestonParams};
use stochastic_rs::quant::OptionType;

use std::cmp::Ordering;
use ndarray::Array1;

#[tokio::main]
async fn main() {

    let r = 0.04;
    let q = 0.06;
    let t = 0.083;

    let strikes_ls: Vec<f64> = vec![5220.318, 6090.371, 6960.424, 7830.477, 8265.5035, 8483.01675, 8700.53, 8918.04325, 9135.5565, 9570.583, 10440.636, 11310.689];
    let spots_ls: Vec<f64> = vec![8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53, 8700.53];
    let vol_ls: Vec<f64> = vec![0.3669, 0.3082, 0.2218, 0.1799, 0.1393, 0.1156, 0.1019, 0.0923, 0.0915, 0.1086, 0.1237, 0.136];
    let markets_ls: Vec<f64> = vec![3499.564, 2632.74, 1765.933, 901.846, 479.055, 279.313, 118.848, 28.79, 4.23, 0.143, 1.799e-5, 1.259e-9];

    let v0 = Array1::linspace(1e-5, 2.0, 5);

    for v in v0.iter() {
      let mut calibrator = HestonCalibrator::new(
        HestonParams {
            v0: *v,
            theta: 6.47e-5,
            rho: -1.98e-3,
            kappa: 6.57e-3,
            sigma: 5.09e-4,
        },
        markets_ls.clone().into(), spots_ls.clone().into(), strikes_ls.clone().into(),
        t, r, Some(q), OptionType::Call,
      );

      // Uncomment to witness NaN Sigma/Rho
      // calibrator.set_initial_params(spots_ls.clone().into(), vol_ls.clone().into(), r);

      let result = calibrator.calibrate();
      let result_unwrap = result.unwrap();

      let minimum_loss = result_unwrap.iter().min_by(|a, b| {
        a.loss_scores.mape.partial_cmp(&b.loss_scores.mape).unwrap_or(Ordering::Equal)
      });

      println!("{:?}", minimum_loss.clone().unwrap().loss_scores.mape);
      println!("{:?}", minimum_loss.clone().unwrap().params);

    }
    }

The markets_ls array was computed with:

    let markets_ls: Vec<f64> = data.iter().map(|x| {

        let bs = BSMPricer::new(x.spot, x.vol, x.strike, r, None, None, Some(q), Some(t), None, None, OptionType::Call, BSMCoc::BSM1973);
        let (c, _) = bs.calculate_call_put();

        return c;

    }).collect()

[dancixx]

@eliebnn I have fixed that if the initial guess is missing you have to call the set_initial_params method, which is a MLE of the Heston params. I have tested your input data and the optimized params are all positive, but for deeper analysis, why is the optimizer not so accurate I need some more time to investigate.

Also, I think that the NMLE of the Heston params is not the most accurate.

[eliebnn]

@dancixx

Let me be more precise - as you can see there is a commented line running calibrator.set_initial_params

1. If I don't run it, aka I keep it commented and I rely on the params input at HestonCalibrator instantiation level as initial guess, I get:

47.288979999331175
HestonParams { v0: 0.035043074836283605, theta: 0.023307280430281397, rho: 0.029265462386466674, kappa: 0.02967394730385698, sigma: 0.03846709839019855 }
66.20941540495458
HestonParams { v0: 0.37227915578672055, theta: -0.15197430375836488, rho: -0.10932777647163476, kappa: -0.12056909932504765, sigma: -0.11646108235334397 }
54.28685598369967
HestonParams { v0: -1.1149357388589973, theta: -2.480726552436385, rho: -1.783973957668885, kappa: -2.1017576315752713, sigma: -1.951665906481375 }
54.24134844899703
HestonParams { v0: -1.2908904357378, theta: -3.0435711593039483, rho: -2.460311091556809, kappa: -2.7477318372936614, sigma: -2.6908963614262706 }
49.40360359951317
HestonParams { v0: -0.4039161192241324, theta: -4.146670889846464, rho: -2.7055853232409834, kappa: -3.507614551413719, sigma: -3.846146800654562 }

Note: negative values are generated.

2. If I do run it, aka uncomment calibrator.set_initial_params, I get:

77.16060137226997
HestonParams { v0: 0.3669, theta: 0.18611966316586462, rho: NaN, kappa: -5.652905371667904, sigma: NaN }
77.16060137226997
HestonParams { v0: 0.3669, theta: 0.18611966316586462, rho: NaN, kappa: -5.652905371667904, sigma: NaN }
77.16060137226997
HestonParams { v0: 0.3669, theta: 0.18611966316586462, rho: NaN, kappa: -5.652905371667904, sigma: NaN }
77.16060137226997
HestonParams { v0: 0.3669, theta: 0.18611966316586462, rho: NaN, kappa: -5.652905371667904, sigma: NaN }
77.16060137226997
HestonParams { v0: 0.3669, theta: 0.18611966316586462, rho: NaN, kappa: -5.652905371667904, sigma: NaN }

Note: NaN values are generated.

Are you able to replicate this by running my script?

[dancixx]

@eliebnn I have checked your example and you are right. I guess (after some debugging) we have some calculation error in the NMLE method which is a maximum likelihood estimation for the initial guess based on this paper: http://scis.scichina.com/en/2018/042202.pdf.

The second issue can be in the optimizer Jacobian matrix that is also implemented based on this paper: https://www.sciencedirect.com/science/article/abs/pii/S0377221717304460

These are fairly formula-heavy algorithms. I have to go through the implementation again, where we have a typo or other bugs. Thx for your patience.

[eliebnn]

Hi @dancixx, have you had some luck with that issue?

[dancixx]

@eliebnn Unfortunately, I'm still struggling with that, but I have already made some progress. Supposedly, I was able to detect the source of the problem, but I need more time to fix this. I probably made a mistake during the partial derivatives for the Jacobian matrix, and because of that, the calibrator will fail.

[eliebnn]

Any chance you can get ideas from the way the Heston model is implemented in the C++ QuantLib library? Saying this but I'm unsure they use the same methodology altogether.

[dancixx]

@eliebnn it seems my assumption was correct — the derivatives were indeed the source of the problem. I have recalculated them, and I am now getting positive values in your example. Please take a look, and thank you for your patience. There is still an error when trying to take an initial guess using maximum likelihood estimation, but I need more time to fix that.

You can find it: abe41e1

[eliebnn]

Hi @dancixx , thanks for the update. I finally had the time to test it.

---

Versions:

• cargo 1.88.0 (873a06493 2025-05-10)
• rustup 1.28.2 (e4f3ad6f8 2025-04-28)
• rustc version is rustc 1.88.0 (6b00bc388 2025-06-23)

I import stochastic-rs via patch.crates-io
[patch.crates-io]
stochastic-rs = { path = "../stochastic-rs" }

Git commit hash of my local stochastic-rs - git rev-parse HEAD

• abe41e1

When running cargo build/run, I get many errors, hence I cannot test the current update to the codebase.

---

Attached are the error logs.
error_logs.txt

[dancixx]

I got the same issue previously when I tried to build using the ai feature flag. Maybe try to disable it, but I already updated the candle related version, and it compiles on my mac. You also can try a force pkg update not just using the cargo clean. I think cargo update will do that.

[eliebnn]

Did some cleanup, and indeed got the script to work.

I am iterating over several V0 via Array1::linspace(1e-5, 2.0, 5);

All calibration outputs, filtered via mape() return more or less the exact same set of parameters which is the initial input.
In other words, the calibration doesn't seems to work as it returns the initial guess as being the best one.

I run exactly the same script as before - just changed the logs - nothing changed in the logic.

Initial guess: Some(HestonParams { v0: 1e-5, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 })
HestonParams { v0: 1e-5, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 }
MAPE Score: 55.05788038751831

Initial guess: Some(HestonParams { v0: 0.5000074999999999, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 })
HestonParams { v0: 0.5000074999999999, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 }
MAPE Score: 68.56082399532299

Initial guess: Some(HestonParams { v0: 1.000005, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 })
HestonParams { v0: 1.000005000037822, theta: 6.470006276895736e-5, rho: -0.0019799999627868456, kappa: 0.0065700000649880205, sigma: 0.0005090000512786943 }
MAPE Score: 72.6267121088258

Initial guess: Some(HestonParams { v0: 1.5000025, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 })
HestonParams { v0: 1.5000025, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 }
MAPE Score: 75.44344585838573

Initial guess: Some(HestonParams { v0: 2.0, theta: 6.47e-5, rho: -0.00198, kappa: 0.00657, sigma: 0.000509 })
HestonParams { v0: 2.0000000000960196, theta: 6.47001439230624e-5, rho: -0.0019799999022290216, kappa: 0.006570000151099736, sigma: 0.0005090001210917701 }
MAPE Score: 78.05184371253307

[dancixx]

@eliebnn I also experienced similar behavior before. The gradient probably gets stuck too early during the optimization process. I will check it, but it seems the negative values are gone now. Thanks for the response.

[eliebnn]

@dancixx did you get the chance to look into the gradient calculation?

[dancixx]

@eliebnn I was to busy last month. I will take a look in the following weeks.

[dancixx]

@eliebnn I have fully rewritten the Heston calibration module in the latest release, maybe you can give it a try.