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Choosing Volatility Inputs for Options on Futures

Article Quant Q&A · Author: ALFRAM
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Summary

The document considers which volatility input to use when pricing options on futures with the Black model or a binomial tree. Its central point is that the appropriate volatility depends on the asset class and on which instrument provides the most relevant market data. In some markets, such as oil, the futures contract may be more liquid than the underlying spot asset, making futures volatility a practical choice.

Forward and spot prices have matching volatility only under assumptions such as deterministic interest rates. That approximation may be reasonable for short-dated equity products, but the answer cautions against relying on it for long-dated contracts or interest-rate products. A second response affirms that futures volatility matches the underlying in the stated setup, but offers no derivation. The discussion is brief and does not give a general pricing procedure or compare model performance, so the modeling assumptions and the market being priced remain important.

Key ideas

  • Choose the volatility input with attention to the asset class and market liquidity.
  • Futures volatility may be more useful when the futures contract is more liquid than spot.
  • Spot and forward volatility coincide under assumptions including deterministic interest rates.
  • That assumption may be unsuitable for long-dated products and interest-rate markets.

Tags

OptionsFuturesVolatilityDerivatives pricing
Full text
# Which volatility to use to price options on futures contract?


# Which volatility to use to price options on futures contract?












I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct.

I am trying to price options on futures for american & european style.

In the latest case, I am using the Black Model.

When looking at the volatility of the contract Ito's lemma gives that the volatility of the future contract is the same as the volatility of the underlying (in the future contract). Is it correct?

Then if I want to use Black Model, I just need to compute the volatility of the futures' underlying.

Options on future are generally american. Then I am using a binomial tree to price my future contracts. Here again the volatility is then determined by the future underlying.

Is that correct?

## Answer by Mark Joshi (score 4, accepted)

https://quant.stackexchange.com/a/16379

it depends on asset class. In some classes, the future is more liquid than the underlying eg oil so it makes more sense to work with its volatility.

Also, the forward price and the spot price only have the same volatility if we assume deterministic interest rates. For short-dated equity type products, this is reasonable. For long-dated products and interest rate products, this is not a good modelling assumption.

## Answer by James Chung (score 1)

https://quant.stackexchange.com/a/32695

When looking at the volatility of the contract Ito's lemma gives that the volatility of the future contract is the same as the volatility of the underlying (in the future contract). Is it correct?

CORRECT

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