Why Forward-Starting Options Can Be Short Volatility of Volatility

Summary

The note explains the intuition for the claim that a long forward-starting option has short exposure to volatility of volatility. A forward-starting option is struck at the money on a future date. To hedge it, the explanation considers selling a currently at-the-money option. If the underlying moves, that hedge becomes out of the money while the forward-starting option remains tied to its future at-the-money strike.

The resulting position combines a long forward-starting option with a short option whose moneyness changes as the market moves. The answer attributes the short volatility-of-volatility exposure to this pattern and says it recurs over the option's life. This is an intuitive hedge-based explanation rather than a derivation or empirical test. It is described as most applicable in stochastic-volatility models, so the document does not establish the claim as a universal result across pricing models or hedge choices.

Key ideas

• A forward-starting option is set at the money on a future date.
• Hedging it with a currently at-the-money option can leave the hedge out of the money after an underlying move.
• The answer links this changing-moneyness hedge to short volatility-of-volatility exposure.
• The explanation is most applicable in stochastic-volatility models.

Tags

# What's the intuition behind "If I am long (short) a forward starting option, I am short (long) vol of vol?"


# What's the intuition behind "If I am long (short) a forward starting option, I am short (long) vol of vol?"












Traders keep telling me this (and sounds very trivial/straightforward), but I don't know why (intuition and mathematically). Could someone help?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/81883

I can address the intuition. Let’s say you are long a forward starting option, meaning an option that gets struck ATM at some future date. You choose to hedge by selling a currently ATM option. Then the underlying market moves. Now you are still long the ATM forward option but short a (now) OTM option. Since OTM options are short vol of vol , you are now short vol of vol. This scenario will occur throughout the life of the forward starting option.

This description is most valid in stochastic vol 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.