Long-Dated Option Calibration and the Limits of Volatility Estimates

Summary

The document considers how to price options with maturities as long as several decades when market quotes for those maturities are unavailable or illiquid. It raises three possible inputs: calibrating to the liquid portion of the volatility surface, using illiquid quotes with adjustments, and incorporating historical data. It does not compare these approaches or prescribe a calibration procedure.

The response emphasizes that, over very long horizons, model error may matter more than uncertainty in the volatility estimate. In particular, companies can undergo substantial capital structure changes, and the response notes that models for those changes are scarce. This is a caution about applying long-term option models, rather than a tested pricing method. The document provides no data, numerical comparison, or evidence that would establish which calibration approach works best, so its main lesson is to treat structural uncertainty as a key limitation.

Key ideas

• Long-maturity options may lack liquid market quotes for calibration.
• Possible inputs include liquid volatility quotes, adjusted illiquid quotes, and historical data.
• Over long horizons, model error can outweigh uncertainty in volatility estimation.
• Corporate capital structure changes are difficult to represent with available models.

Tags

# Model calibration to illiquid assets when pricing options with long maturities


# Model calibration to illiquid assets when pricing options with long maturities












Let us assume one is interested in pricing an option with a very long maturity (up to 20 or 30 years) on a liquid underlying.

The market won't have liquid quotes for the higher maturities. Still you would like to incorporate some assumptions on the long-term vol in the market.

What are the best approaches here ?

Some generic ideas/thoughts

- Calibrate to the liquid vol surface and neglect the lack of information for long maturities

- Use the illiquid quotes but with some adjustments (perhaps addying some margin)

- Incorporate historical data

## Answer by Brian B (score 2, accepted)

https://quant.stackexchange.com/a/10357

At long maturities, the real problem tends more to be model error than volatility estimation: over that kind of time period most companies undergo significant capital structure changes, for which there are very few models.

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