Choosing Option Quotes for Heston Model Calibration

Summary

The document discusses selecting option implied volatilities and strikes as inputs or starting values for calibrating the Heston stochastic volatility model. It raises whether a one-year implied volatility is appropriate for the model's long-run variance parameter and how far out of the money an option can be before its quote becomes unsuitable. The answer distinguishes the Heston variance process from constant-volatility Black–Scholes assumptions, while allowing that a longer-dated implied volatility might still serve as an initial guess for optimization.

For strike selection, the response points to quote quality as a concern: far out-of-the-money options, especially beyond roughly three standard deviations, may have rounded or unreliable prices. It also cautions that Heston does not capture fat tails well, making extreme strikes a poor fit for calibration. A proposed practical range is around one to two standard deviations, with observations spanning maturities. The post is advisory rather than a worked calibration study; it gives no empirical comparison or universal moneyness threshold, and the number and quality of observations depend on the calibration setup.

Key ideas

• Heston's stochastic variance dynamics differ from the constant-volatility Black–Scholes assumptions behind implied volatility.
• A longer-dated implied volatility may be used as an optimization starting value, but it is not automatically the long-run variance.
• Far out-of-the-money quotes can be distorted by rounding or poor market quality.
• Heston's limited representation of tail behavior is a reason to avoid relying heavily on extreme strikes.
• The answer suggests using options around one to two standard deviations and including multiple maturities.

Tags

# Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?


# Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?












I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.

Firstly, why would it be unreasonable to take implied vol of a 1 year contract, and use that as your long-run vol, $\theta$ of the Heston model?

Secondly, as a contract becomes more OTM, its implied vol is no longer useful for Heston calibration. So in general, when people discuss ATM options, what's the range around the spot vs the strike? 1%, 5%?

## Answer by Alex D (score 2)

https://quant.stackexchange.com/a/76497

A1: Volatility implied by what model? :)

A2: Check what the volatility smile is and how it affects your model.

UPD: As @frido insisted, I would add more details.

#### "Why not 1 year IV"

Because processes are different. CIR distribution (Heston) is different from brownian motion with constant IV (Black-Scholes). But you can try 1 year IV as an initial value for callibration.

#### "How far the OTM?"

From a first glance, I see 2 main reasons not to use far OTM options for calibration.

First of all, it is a matter of quality of your option board. Far OTM options (> 3*sigma) tend to be "rounded" or inadequate. As a result, you would calibrate on option prices affected by technical details.

Second, Heston model has no idea about "fat tails".

What is the minimum? Heston model has 5 parameters (kappa, theta, v0, rho, sigma). So, you need at least 5 points to optimise. :)

I would recommend using 1 or 2 sigma and then go deeper in time.

#### Links

The way to calibrate Heston model I would recommend: https://www.maths.univ-evry.fr/pages_perso/crepey/Equities/051111_mikh%20heston.pdf

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