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Monte Carlo Discretization for Heston Model Calibration

Article Quant Q&A · Author: Neeraj
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Summary

The discussion considers whether Monte Carlo simulation can calibrate the Heston stochastic volatility model and which discretization to use. One answer recommends calibrating vanilla European options with the model’s known characteristic function and Fourier methods, which are described as much faster, then using Monte Carlo to price path-dependent exotic options after calibration.

For cases where Monte Carlo calibration is necessary, the answers suggest Euler–Milstein and Andersen’s Quadratic Exponential scheme as discretization choices. The exchange offers no comparison of their accuracy, convergence, or implementation tradeoffs. A commenter argues that relying on Monte Carlo for exotic pricing should support using it for calibration too, but this is an opinion rather than evidence that the approaches are equally efficient or reliable. The practical lesson is to weigh calibration speed and the available characteristic function against the need for simulation-based methods.

Key ideas

  • The Heston model’s known characteristic function makes Fourier-based calibration of vanilla options a faster alternative to Monte Carlo.
  • Monte Carlo is commonly used to price path-dependent exotics after calibration to vanilla options.
  • Euler–Milstein is suggested as a possible Heston simulation discretization for Monte Carlo calibration.
  • Andersen’s Quadratic Exponential scheme is offered as another discretization choice.
  • The discussion does not compare the schemes’ accuracy or establish when Monte Carlo calibration is preferable.

Tags

Derivatives pricingVolatilityOptionsStatistics
Full text
# Heston model calibration using Monte Carlo


# Heston model calibration using Monte Carlo












Hi can we calibrate Heston using Monte Carlo?.

Can you suggest good discretization scheme if we use Monte Carlo to calibrate ?

I want to avoid Fourier transformation

## Answer by Frido (score 3)

https://quant.stackexchange.com/a/81694

Sure you can calibrate Heston using Monte Carlo. But you should not try to avoid the Fourier transform method as it is much quicker since for the Heston model the characteristic function is known.

Monte Carlo is usually used after calibration to vanilla European options when, as a next step, you want to price (path-dependent) exotic options.

If you insist on using MC to calibrate, which I do not recommend unless there is no other possibility, then you can start using the Euler-Milstein scheme as discretization scheme.

## Answer by Jesper Tidblom (score 1)

https://quant.stackexchange.com/a/81695

Another good discretization scheme for the Heston model is the so called Quadratic Exponential scheme by L. Andersen. This scheme is described in the article "Efficient Simulation of the Heston Stochastic Volatility Model".

But, as Frido says, using Monte Carlo for calibration is not really recommended.

## Answer by marie albertini (score 0)

https://quant.stackexchange.com/a/81698

the idea of using a MODEL (stochastic vol or else....) is to price non standard instruments....which is when you are going to need ..monte carlo.

imagine that your exotic option reduces to a plain vanila after some events (ki, ko, settings...), you are still going to price it using monte carlo and you should trust it to give you the right price !

so not trusting it to calibrate makes non sense...i.e if monte carlo is not recommanded for plain vanila, why should it be for exotics (but your model is there to price exotics after being calibrated in the first place...you are running after your own tail).

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