Charm
Rate of delta change over time
What is Charm?
Charm Charm is a second-order Greek that measures the rate at which an option's delta changes as time passes, with all other factors held constant. Also known as delta decay or DdeltaDtime, charm quantifies how much your directional exposure shifts simply from the passage of one day. It is one of the most practically important second-order Greeks because it directly affects hedging requirements for any options position held overnight. How it works: As time passes, out-of-the-money options lose delta (moving toward 0) while in-the-money options gain delta (moving toward 1.0 for calls or -1.0 for puts). At-the-money options have near-zero charm because their delta stays anchored around 0.50 until very close to expiration. Charm accelerates as expiration approaches, meaning delta shifts become larger and more rapid in the final days of an option's life. This is because time decay causes the probability distribution of the stock to narrow, making it increasingly clear whether an option will finish ITM or OTM. For example, consider a slightly OTM AMZN $195 call with 10 days to expiration and a delta of 0.40. If charm is -0.03, then tomorrow the delta will be approximately 0.37 (assuming AMZN's price is unchanged). Over the next 5 days, charm might shift the delta down to about 0.25, substantially reducing the call's directional exposure. A market maker hedging this position would need to sell shares each day to stay delta-neutral, even if AMZN's price has not moved. Charm-driven hedging flows are a major source of mechanical buying and selling pressure in the market. When large amounts of open interest are concentrated in OTM options near expiration, charm causes rapid delta changes that force market makers to continuously rebalance their hedges. This is why the final days before major expirations often see unusual price pinning or directional drift: dealer charm hedging can push the stock toward or away from heavily populated strikes.
Complete Definition
Charm is a second-order Greek that measures the rate at which an option's delta changes as time passes, with all other factors held constant. Also known as delta decay or DdeltaDtime, charm quantifies how much your directional exposure shifts simply from the passage of one day. It is one of the most practically important second-order Greeks because it directly affects hedging requirements for any options position held overnight. How it works: As time passes, out-of-the-money options lose delta (moving toward 0) while in-the-money options gain delta (moving toward 1.0 for calls or -1.0 for puts). At-the-money options have near-zero charm because their delta stays anchored around 0.50 until very close to expiration. Charm accelerates as expiration approaches, meaning delta shifts become larger and more rapid in the final days of an option's life. This is because time decay causes the probability distribution of the stock to narrow, making it increasingly clear whether an option will finish ITM or OTM. For example, consider a slightly OTM AMZN $195 call with 10 days to expiration and a delta of 0.40. If charm is -0.03, then tomorrow the delta will be approximately 0.37 (assuming AMZN's price is unchanged). Over the next 5 days, charm might shift the delta down to about 0.25, substantially reducing the call's directional exposure. A market maker hedging this position would need to sell shares each day to stay delta-neutral, even if AMZN's price has not moved. Charm-driven hedging flows are a major source of mechanical buying and selling pressure in the market. When large amounts of open interest are concentrated in OTM options near expiration, charm causes rapid delta changes that force market makers to continuously rebalance their hedges. This is why the final days before major expirations often see unusual price pinning or directional drift: dealer charm hedging can push the stock toward or away from heavily populated strikes.
Frequently Asked Questions
What does Charm measure in options?
Charm measures how an option's delta changes as time passes, with the stock price held constant. OTM options lose delta over time (charm pulls delta toward 0), while ITM options gain delta (charm pulls delta toward 1.0). This effect accelerates as expiration approaches.
How does Charm affect market maker hedging?
Market makers must rebalance their delta hedges as charm shifts their position's delta over time. If they are short OTM calls that are losing delta, they must sell shares to reduce their hedge. These daily hedging adjustments can create consistent directional flows in the underlying stock, especially near expiration.
When is Charm most significant?
Charm is most significant in the final 5-7 days before expiration and for options that are slightly OTM or slightly ITM. ATM options have near-zero charm until very close to expiration. Charm is also larger when implied volatility is low, because the narrower probability distribution makes delta changes more pronounced as time passes.
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