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# Charm (Delta Decay)

## What Is Charm (Delta Decay)?

Charm, or delta decay, is the rate at which the delta of an option or warrant changes with respect to time. Charm refers to the second order derivative of an option's value, once to time and once to delta. It is also the derivative of theta, which measures the time decay of an option's value.

### Key Takeaways

• Charm, or delta decay, measures the change in an option's delta as time passes, all else being equal.
• Charm values range from -1.0 to +1.0, with in-the-money options tending toward 100 delta and out-of-the-money options toward zero as expiration approaches.
• Options traders take note of their position's charm in order to maintain delta neutral hedging as time passes, even if the underlying stays put.

## Understanding Charm (Delta Decay)

Charm shows how much an option's delta changes each day until expiration. An option's delta is its change in value (premium) given a change in price in the underlying asset. Thus, an option with a +.50 delta will gain fifty cents in value for every dollar that the underlying rises in price. Delta, however, is not static.

Gamma, for instance, measures an option's delta change as the underlying price moves—so if an option originally has +0.50 delta and the underlying moves up by a dollar, if it had a gamma of .10, then the new delta is +0.40. Delta also changes (decays) as time passes, all else being equal. That is what charm measures.

Charm values range from -1.0 to +1.0. In the money (ITM) calls and out of the money (OTM) puts have positive charms, while ITM puts and OTM calls have negative charms. At the money options have a charm of zero, but delta decay towards either zero or 100 accelerates for options that are not at the money as expiration approaches.

Charm is relevant for options traders, and primarily to those using options to hedge. Because the market closes for two days each weekend, the charm’s effect is magnified. When the market closes Tuesday at 5 p.m. ET and reopens Wednesday at 8 a.m., charm has only half a day of effect. When the market closes Friday at 5 p.m. and reopens Monday at 8 a.m., two and a half days pass without trading the underlying security. Options traders, especially those managing delta-hedged positions, must pay close attention to their charm on Friday as it impacts their options action on Monday.

Some portfolios are self-hedging against charm risk. Say, for example, an investor owns a 15% delta call and a -15% delta put. The charm on these options is offset, leaving them charm-neutral. Since charm makes the option delta tend toward zero over time for OTM options, the call delta falls over time and the put delta rises toward zero. The position is called a strangle because it is a long out-of-the-money call and put.

## Charm Examples

As an example, assume that an investor has an out of the money call option with a delta of 15% and a normalized charm of -1. Other things being equal, when the investor looks at the call the next day, delta will be 14%.

As another example, say a trader places a delta-hedged call option on Friday with a charm of 1 and 15% delta; they are short 15 lots of the spot product for every 100 calls they own. By Monday at 8 a.m., the call delta may have decreased to 12.5%; two and a half days have passed multiplied by the charm of 1. The trader’s delta hedge is no longer accurate; they are short too much of the underlying security. If the spot market opens higher on Monday, the trader has to buy back deltas to cover their position and reestablish a delta-neutral stance. Special attention is needed around a charm’s expiration time, as it may become very dynamic.

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