Calibrating Heston Models for Autocall Portfolios

Summary

The note explains how to choose volatility-surface inputs when calibrating a model for autocallable products. Its central recommendation is to calibrate one model to the autocalls held in the portfolio, reflecting that hedging is generally managed at portfolio level rather than by fitting each product separately.

It identifies knock-in and knock-out levels as important regions of the surface. The knock-in barrier can matter more than the strike, while the knock-out level has sensitivity resembling a digital option. The suggested calibration range runs from below the portfolio’s lowest knock-in barrier to above its highest autocall level, with extra weight on volatility points near both barrier types and a smooth surface in those areas. This is practitioner guidance, not a demonstrated calibration study: the note offers no data, quantitative comparison, or details on calibration objectives. The questioner mentions Monte Carlo with Heston, but the answer does not give Heston-specific implementation steps or establish that this guidance is optimal for every portfolio.

Key ideas

• Calibrate the model against the autocalls in the portfolio when hedging is performed at portfolio level.
• Include volatility data from below the lowest knock-in barrier to above the highest autocall level.
• Give particular attention to volatility near knock-in and knock-out barriers.
• Keep the volatility surface smooth around the levels that drive barrier sensitivity.
• Treat the recommendations as qualitative guidance rather than a tested comparison of calibration methods.

Tags

# Autocall Calibration


# Autocall Calibration












I'm trying to price autocalls.

In theory my pricing method is ok (I followed Bouzoubaa's book procedure) but I'm not sure I read anything on calibration of autocalls. Basically my question is what part of the vol surface should I use ? My coupon digits can range from 50% to 90% and the same range for the put down and in barrier.

Let's say i do 2 pricings. First one coupon barrier 50%, second one coupon barrier 80%. The put remains the same, strike 100%, barrier 80%. Should I calibrate 2 different models ? I mean, first one I should use vol surface with strike ranging from 50% to 100% and second one, the surface from 80 to 100% ?

I'm simulating Monte Carlo paths with Heston model, in case this could be relevant

## Answer by alexprice (score 1)

https://quant.stackexchange.com/a/53035

Your model ideally should be calibrated to all autocalls in your portfolio , as hedging is usually done on portfolio level.

Autocalls have sensitivity to KI barrier, and KO barrier (autocall level, kinda digital option thus high sensitivity to vol surface near the KO level).

KI Barrier is more important then strike level. Thus your model should ideally be calibrated from below lowest KI barrier to higher than highest Autocall level in autocall portfolio.

Make sure that Vol surface is smooth near KI and KO levels. And for calibration you can put more weights to vol points near KI barrier levels and KO levels.

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