Numerical Integration Methods for the Heston Call Pricing Formula

Summary

The document asks how to evaluate the integral in the semi-closed Heston formula for call options. Its answer says Monte Carlo simulation can approximate the integrals, while Newton-Cotes formulas and Gaussian quadrature are also possible numerical methods. It points to an external worked solution, but the details of that solution are not reproduced in the text.

An example reports call and put prices using parameters attributed to a cited source. The post does not provide the parameter values, implementation details, accuracy checks, or a comparison among the numerical methods in the material shown. It therefore illustrates that the integral can be approximated and gives sample prices, but is not sufficient on its own to reproduce the calculation or judge the numerical error.

Key ideas

• The integral in the semi-closed Heston option pricing formula can be approximated numerically.
• Monte Carlo integration is one proposed approach, alongside Newton-Cotes formulas and Gaussian quadrature.
• The document reports example call and put prices based on parameters from a cited source.
• The shown text omits implementation details and error analysis, limiting reproducibility.

Tags

# Evaluation of the semi-closed Heston pricing formula for call options


# Evaluation of the semi-closed Heston pricing formula for call options












I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this purpose.

It would be great, if someone could provide an example, where this is computed or can give a paper, where an explicit example is given. Maybe a Matlab code can also be helpful in this case.

I am refering to equation (18) on page 331 of the paper

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

Thanks.

Regards,

Arjen

## Answer by user16891 (score 3)

https://quant.stackexchange.com/a/18894

I have approximate the integrals by Monte Carlo Method but you can use several method such as Newton-Cotes formulas and Gaussian quadrature.

### Function

### Example

### Solutions

Call =

34.0976

Put =

```
4.8941
```

Parameters were extracted from Jianwei Zhu(2008),Page 10,Table 4

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