Choosing Heston Pricing Methods for European and Non-European Options

Summary

The discussion explains why Heston implementations may use a Fourier-based method during calibration and Monte Carlo for later pricing. Under Heston, European option prices have a quasi-analytical representation, so numerical integration methods such as FFT can approximate the required integrals efficiently. The choice among numerical methods depends on the use case, with computational speed often a practical concern.

That shortcut is limited to European options. For products without a usable quasi-analytical formula, Monte Carlo or another suitable method may be needed. A simpler European pricing method can sometimes help narrow a calibration search before using a more appropriate approach for the target product. The response presents this as a possible workflow rather than a universal prescription; the author notes that the calibration shortcut is based on analogous experience, not personal use of that exact procedure. It gives no benchmark or quantitative comparison of FFT and Monte Carlo performance.

Key ideas

• Heston has a quasi-analytical pricing representation for European options.
• Numerical integration methods, including FFT approaches, can approximate the integrals in that representation.
• Method choice depends on the pricing task, and speed is often a key consideration.
• The European-option approach may not apply to products without a suitable closed-form representation.
• A simpler pricing method can sometimes narrow calibration searches before a more suitable method is used.

Tags

# Heston Monte Carlo or FFT Pricing


# Heston Monte Carlo or FFT Pricing












I am trying to better understand the Heston model and its implementation. It seems like a lot of people use the FFT method for calculating the call prices during the Heston calibration, but the Monte Carlo method is used to calculate the prices with the calibrated parameters. What is the point in this? Why not just use the FFT method for calculating both prices?

## Answer by Stéphane (score 1)

https://quant.stackexchange.com/a/53741

The big advantage of the Heston (1993) model is that it admits a quasi-analytical formula for the pricing of European options. So, obviously, if you're going to price European options, you should be using some kind of numerical method to approximation the integrals in the quasi-analytical formula. The exact method you use will depend on the case at hand and what matters most -- usually, speed is of the essence.

However, that only works for European options. Outside of that small pond, it might be possible in some cases to think that your European option is a good starting point for calibration. I have never done this personally, but I have done similar things (use simpler methods to reduce my searching time before doing things in a more Kosher manner).

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