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In the asset management industry, many reports contain liquidity metrics such as the no. of days to liquidate 95% of a position, based on a certain participation rate.

If that position is a stock or a bond, this is straightforward.

How would we calculate this number of days with a position that's a derivative (a simple call option for instance)? Do we take trading volume for the option or the notional? Numerical example welcome.

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You are right to be concerned about this. The liquidity of many options is not as good as many people imagine. I have personally been in situations where a fund needed to liquidate a large option position and it was difficult to do. Once market makers detect a liquidity-crisis situation they pull back and the situation worsens. The liquidity of option markets is time varying. If you cannot get out of your position immediately you have to cross-hedge in other markets and/or delta hedge with the underlying (which is always more liquid than the option); essentially you have to become a market maker yourself.

The simplest approach to measurement is to compare your position size to the normal volume for the option. Still you have to keep in mind that the option volume will reduce at the next financial crisis.

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