Choosing Heston Parameter Bounds for Neural-Network Calibration

Summary

This thesis-related question asks how to choose bounds for the Heston model parameters kappa, theta, sigma, and rho when generating synthetic data to train a neural network for calibration. It compares one published set of ranges, described as excluding mathematically feasible but economically unacceptable solutions, with wider or differently scaled ranges proposed elsewhere. The author seeks reasons for those differences and guidance on which bounds suit particular purposes.

The document raises a practical calibration-design issue but does not provide an answer, evidence comparing candidate ranges, or a recommended parameter set. It therefore highlights that bounds are modeling choices tied to economic plausibility and the intended training dataset, rather than resolving how to set them. Readers would need to consult the cited studies and assess the parameter domain against their market data and calibration objectives; the question alone does not establish that any listed bounds are generally preferable.

Key ideas

• The question concerns bounds for kappa, theta, sigma, and rho in Heston calibration.
• The bounds are intended for generating synthetic training data for a neural network.
• The cited ranges differ, and the document asks why those choices vary.
• One cited rationale is to exclude mathematically feasible but economically unacceptable parameter solutions.
• The document does not recommend a range or compare calibration outcomes.

Tags

# Parameters bounds for Heston model calibration


# Parameters bounds for Heston model calibration












Still working on my master thesis and I have a question I have been looking at for some time but can't find a good reason.

I am looking to follow the steps of Horvath et al. (2019) in order to calibrate the heston model to market data using neural networks. At the moment I am focusing on the creation of my artificial dataset that will be used to train the model, thus trying to get a good understanding of the bounds of the parameters kappa,theta,sigma,rho I am trying to generate.

In his paper, Crisóstomo (2014) gives bounds that allow to avoid possible solutions that while mathematically feasible, are not acceptable in an economic sense. His bounds are:[0,20][0,1][0,1][-1,1]. But in other papers I am reading, they propose the bounds [0.001,15][0.001,6][0.005,4]and [-0.999,0.999]. Is there any specific reasons for this, or else, do you know (or have a reference paper) what bounds should be used and for what specific reasons ?

Thanks a lot in advance

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.