Using Local Volatility to Price an Autocallable

Summary

The document raises implementation questions about pricing an autocallable product with a local volatility model. Its payoff description includes coupons accumulated at observation dates and paid when an autocall barrier is reached, along with a short down-and-in put exposure at maturity. The proposed workflow is to infer local volatility from implied volatility using Dupire’s formula, then calibrate the model against vanilla option prices by minimizing an error measure.

The questions highlight two practical challenges: deciding which model parameters to optimize and valuing the bond-like cash flows using autocall probabilities. The post asks whether probability-weighted bond values are appropriate and seeks implementation examples, while also mentioning rough volatility as an alternative. It provides no solution, calibration evidence, or pricing results, so it serves mainly as a statement of modeling issues rather than a complete method. The appropriate calibration parameters and valuation approach depend on the product terms, market inputs, and modeling assumptions.

Key ideas

• The described payoff accumulates coupons at observation dates and pays them when an autocall barrier is reached.
• At maturity, the product includes exposure to a short down-and-in put.
• The proposed model workflow uses Dupire’s formula to derive local volatility from implied volatility and calibrates against vanilla options.
• The document leaves the calibration parameters and treatment of autocall probabilities unresolved.

Tags

# Local volatility model for autocallable pricing


# Local volatility model for autocallable pricing












I am working on a pricer for an Autocallable product in Python. Coupons are accumulated at each observation and paid once the AC barrier is reached. At maturity, short down-and-in put. I am trying to price it with local volatility model, but have some trouble to implement it. I have several questions :

- I guess I would like to transform implied volatilities to local volatilities with the Dupire formula, then price vanilla options and calibrate to reduce some error metric. But what would be the parameters to optimize ?

- How to price the bond part with autocall probabilities (and get those probabilities) ? should I weight several bonds with those probabilities ?

Does anyone has some code reference for such a model (language does not matter) that could help me ?

I am also open to other suggestions of model implementation for this product such as rough volatility, etc.

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