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Numerical Integration Choices for Heston Option Pricing

Article Quant Q&A · Author: Matthias
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Summary

The document concerns numerical evaluation of the integral used to price a call option under the Heston stochastic volatility model. The question asks whether Simpson’s rule or Gauss–Legendre quadrature is suitable and seeks MATLAB or Scilab implementations.

The responses point to existing implementations of both integration methods and to a Heston model reference that includes code. They do not compare the methods’ accuracy, convergence, computational cost, or behavior for particular model parameters. As a result, the material is a pointer to implementation resources rather than a worked numerical procedure; a user would still need to choose integration bounds and settings and validate the resulting option prices.

Key ideas

  • Heston option pricing can require numerical approximation of an integral.
  • Simpson’s rule and Gauss–Legendre quadrature are presented as candidate methods.
  • The responses provide pointers to code resources but no method comparison or worked example.
  • Numerical settings and accuracy still need to be checked for the chosen parameters.

Tags

OptionsVolatilityDerivatives pricingStatistics
Full text
# Numerical computation of Heston model Integral: Simpsone Rule or Gauss-Legendre Method


# Numerical computation of Heston model Integral: Simpsone Rule or Gauss-Legendre Method












I want to price a call option using the Heston model for a given set of parameters.

theory from URL: http://elis.sigmath.es.osaka-u.ac.jp/research/Heston-original.pdf

The integral equation (18) needs to be approximated.

I'd like to either use the Simpson Rule or Gauss-Legendre method for it.

Does anybody have the matlab or scilab codes for it ?

## Answer by Robert Szóstakowski (score 0)

https://quant.stackexchange.com/a/19608

I guess this it, but you need to create an account:

Gauss- Kegendre method http://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes

Simpsone Rule http://www.mathworks.com/matlabcentral/fileexchange/28726-simpson-s-rule-integration/content/simpsons.m

## Answer by Sam Palmer (score -1)

https://quant.stackexchange.com/a/28058

Sorry if this is late, but this is the bible of Heston (and it has code) https://www.amazon.co.uk/Heston-Model-Extensions-Matlab-Finance-ebook/dp/B00EMADBN2/ref=sr_1_1?ie=UTF8&qid=1468410988&sr=8-1&keywords=Heston+matlab

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.