Calibrating Heston and Local Volatility Models to Option Data

Summary

The document frames a calibration problem for pricing an equity exotic derivative under Heston and local volatility models. It asks whether to fit model prices directly to observed American option quotes, or first infer implied volatilities from those quotes and construct a volatility surface before calibrating against European option prices. The second route would use SVI or SSVI to represent the surface, with interpolation and extrapolation to fill gaps.

The text does not provide an answer, comparison, or empirical results, so it does not establish which approach is preferable. It highlights practical modeling choices that need resolution: American option pricing and implied-volatility inversion, the reliability of a fitted surface away from observed strikes and maturities, and whether prices from different exercise styles are comparable calibration targets. The document is best read as a statement of competing calibration workflows rather than a recommendation or validated procedure.

Key ideas

• The calibration target is an equity exotic derivative priced under Heston or local volatility dynamics.
• One proposed method fits model prices directly to observed American option quotes.
• Another method builds an implied-volatility surface from American quotes and calibrates using European prices.
• SVI or SSVI can parameterize the surface, while interpolation and extrapolation extend it beyond observed quotes.
• The document poses the alternatives but gives no conclusion or supporting evidence.

Tags

# Procedure of model calibration


# Procedure of model calibration












Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the following approaches make sense?

- Directly minimize distance between model derived (Heston/local vol) American option prices and observed market quotes.

- Use SVI/SSVI and some interpolation/extrapolation to extend the BS-implied volatility surface that you obtain by inverting American option market quotes (using e.g. a CRR tree). Then derive Eurpean option prices from the surface using BS and minimize distance with the model derived European option prices.

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