Initial Guesses and Optimization Methods in Heston Calibration

Summary

The document asks whether poor initial parameter guesses can explain a badly fitting Heston calibration and how to choose better starting values. Its responses emphasize that sensitivity depends on the optimization algorithm: local deterministic methods, such as gradient approaches, can depend strongly on the starting point, while global stochastic methods such as simulated annealing are described as less dependent on it.

The accepted response points readers toward an external practical implementation and adaptive simulated annealing code as resources for checking their results. Another cited reference covers Heston implementation and calibration. The document does not provide parameter bounds, a recipe for selecting initial values, or evidence comparing calibration outcomes. It also does not establish whether the reported mismatch came from initialization, the crude Monte Carlo setup, or another implementation issue, so its advice is conceptual and directs readers to further material.

Key ideas

• Local deterministic optimization can be sensitive to the initial parameter guess.
• Global stochastic methods such as simulated annealing are described as less dependent on starting values.
• The responses recommend consulting practical Heston calibration implementations to check a calibration setup.
• No specific initial parameter values or comparative calibration results are provided.

Tags

# Answer by user7056 (score 3, accepted)


# Heston - How important are the initial guess in calibration and if it is very important, what would be a good way to get initial guess?












So I have been trying to implement a simple Heston calibration using crude MC with 10k scenarios and 1000 time steps and the best I could get is 3x of the observed implied volatility.

I suspect it has something to do with the way my initial guess worked, and therefore, I am just wondering:

- Is the initial guess very critical (that a not-so-great initial guess could give you 3x the differences)

- If it is, how can I get a good initial guess?

## Answer by user7056 (score 3, accepted)

https://quant.stackexchange.com/a/8263

To check your results, you might try "The Heston Model: A Practical Approach with Matlab Code" by Nimalin Moodley, http://math.nyu.edu/~atm262/fall06/compmethods/a1/nimalinmoodley.pdf , in particular the www.ingber.com open source C++ code for Adaptive Simulated Annealing (+ SWIG to wrap/parse it to the language you are using)

## Answer by vonjd (score 2)

https://quant.stackexchange.com/a/8268

It depends on the used optimization algorithm, esp. whether they act locally or globally.

Just to give you some ideas:

- Local (deterministic) algorithms (e.g. gradient methods): a good initial guess is crucial.

- (Global) stochastic algorithms (e.g. simulated annealing): the initial guess is irrelevant.

You can find more here: Heston’s Stochastic Volatility Model Implementation, Calibration and Some Extensions by Sergei Mikhailov, Ulrich Nögel

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