Using Parkinson Range and Historical Volatility to Guide Gamma Hedging

Summary

The document asks about a proposed relationship between the Parkinson number, a range-based volatility measure, and historical volatility, and whether their comparison can guide hedge timing for a long gamma position. It relays a claim that a higher Parkinson number calls for more frequent delta hedging, then offers a brief answer focused on the opposite case: when the Parkinson number is below the stated volatility multiple, price changes are said to show a self-regressing tendency.

Under that interpretation, after a large move a long gamma trader should hedge delta promptly because a reversal could erode gains while theta continues to cost money. The answer does not derive the relationship, define how either measure should be estimated, or provide empirical evidence. It therefore offers a possible intuition for hedge timing, not a general rule validated across markets or conditions.

Key ideas

• The document considers using a comparison between a range-based volatility measure and historical volatility to inform hedge timing.
• The response associates a lower Parkinson reading relative to the stated multiple with price reversals.
• Under that interpretation, a long gamma trader may want to adjust delta soon after a large move.
• Theta decay can offset gains if the price reverses before the position is hedged.
• The answer gives no derivation or empirical evidence for the proposed relationship.

Tags

# Relation between Parkinson number and historical volatility


# Relation between Parkinson number and historical volatility












In his book 'Dynamic Hedging', Nassim Taleb gives the relation: P = 1.67*historical volatility, where P is the Parkinson number.

What is the basis of this relationship. Does this hold under special situations, or always? He goes on to say that if P is higher than 1.67*HV, then the trader needs to hedge a long gamma position more frequently. Otherwise,he can lag the adjustment, letting the gammas run.

Why is this?

## Answer by 大空驴 Big Short Donkey (score 2)

https://quant.stackexchange.com/a/60804

I do not know if there are still people following this question.

If the P is lower than 1.67HV, then we can conclude that there is a self-regression effect in markets. As a result, if a trader, who has long gamma, facing a relatively large price change, he needs to hedge his delta as soon as possible because the price is more likely to move backward and the trader would lose money in his short theta position.

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