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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
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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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  • $\begingroup$ do yo perhaps have any literature you could refer me to ? - something like "Model Error and long term projection" (the title is pure fiction ^^) $\endgroup$
    – Probilitator
    Feb 25, 2014 at 6:28
  • $\begingroup$ Sorry, nothing comes to mind. Capital structure tends to be considered, at best, abstractly in the academic literature and I have never seen an academic paper involving empirical data of capital structure changes. Among hundreds of thousands of papers it must exist, but I've never looked hard enough find any such thing. $\endgroup$
    – Brian B
    Feb 25, 2014 at 17:18

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