Choosing Stable Numerical Methods for Heston Option Pricing

Summary

The document describes a research need for reliable Heston option prices, especially for options far out of the money. The author reports that numerical instability in a current implementation produces slightly negative or oscillating prices, which then undermines implied-volatility calculations and distorts the plotted volatility smile.

The request is for free software, preferably accessible from Python, that can price Heston options accurately across strikes. It mentions existing implementations and identifies practical concerns with alternatives, including cumbersome setup, documentation, maturity inputs tied to calendar dates, and lack of Python bindings. The text does not provide a comparison, solution, benchmark, or evidence that any named package meets the accuracy requirement; it frames tool selection as an unresolved research problem. Its central lesson is that pricing stability, language integration, maturity conventions, and usability all matter when calibrating a stochastic-volatility model.

Key ideas

• Unstable Heston prices can become negative or oscillate, especially for far out-of-the-money options.
• Price errors can contaminate implied-volatility calculations and the resulting smile.
• A useful pricing library should support accurate prices across strikes and fit the research workflow.
• The document raises software selection criteria but does not identify or validate a solution.

Tags

# Robust and free Heston pricing software


# Robust and free Heston pricing software












For a PhD research paper, I need to calibrate Heston. So far, I use

> Dale Roberts R-Code: https://github.com/daleroberts/heston/blob/master/heston.r

for computing prices from which I invert IV using

> PyVolLib: https://github.com/vollib/py_vollib

As can be seen from the plotted smile, (deep) OTM data is not good. The problem can be traced down to the numerical instability of the Heston pricer which returns slightly negative and/or oscillating prices.

Hence, I am looking for software that

- prices Heston accurately also for OTM options

- should be free (poor PhD student in MathFinance)

- ideally in Python as the rest of my code is in Python

QuantLib (https://www.quantlib.org) seems like a solution but

- there is a ton of boilerplate code even for simple tasks and the documentation is not exactly friendly

- I need time to maturity as an input variable but it seems QuantLib only takes exact calendar days for the maturity.

I am also aware of Premia's (https://www.rocq.inria.fr/mathfi/Premia/index.html) available software but they also don't provide Python bindings.

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.