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