What is Charm (Delta Decay)?
Charm, or delta decay, is the rate at which the delta of an option or guarantee changes with respect to time. Charm refers to the second-order derivative of the value of an option, once at a time and once at delta. It is also the derivative of theta, which measures the time for an option’s value to fall.
- Charm, or delta decay, measures the change in an option’s delta over time, all other things being equal.
- Charm values range from -1.0 to +1.0, with in-the-money options trending toward 100 delta and out-of-the-money options toward zero as expiration approaches.
- Option traders take note of the allure of their position to maintain a delta neutral hedge over time, even if the underlying remains fixed.
Understanding Charm (Delta Decay)
Charm shows how much the delta of an option changes each day until expiration. The delta of an option is its change in value (premium) given a change in the price of the underlying asset. Therefore, an option with a delta of +.50 will earn fifty cents in value for every dollar the underlying price rises. Delta, however, is not static.
Gamma, for example, measures the delta change of an option as the underlying price moves; therefore, if an option originally has a delta of +0.50 and the underlying goes up one dollar, if it had a gamma value of 0.10, then the new delta is +0.40. . Delta also changes (decays) as time passes, everything else is the same. That’s what charm measures.
Charm values range from -1.0 to +1.0. In-the-money (ITM) calls and out-of-the-money (OTM) put options have positive charms, while ITM put options and OTM calls have negative charms. In-the-money options have a zero charm, but the delta drop to zero or 100 accelerates for non-money options as expiration approaches.
The charm is relevant for option traders and mainly for those who use options to protect themselves. Because the market is closed for two days every weekend, the effect of the charm is magnified. When the market closes on Tuesday at 5 p.m. ET and reopens on Wednesday at 8 a.m., the allure has only half a day in effect. When the market closes at 5pm on Friday and reopens at 8am on Monday, two and a half days go by without trading the underlying security. Options traders, especially those managing delta hedged positions, should pay close attention to its charm on Friday as it affects their options action on Monday.
Some wallets are self-hedging against charm risk. Say, for example, an investor owns a 15% delta call and a -15% delta put option. The charm of these options is offset, leaving them charm neutral. Since the charm causes the delta of the option to go to zero over time for OTM options, the delta of the call falls with time and the delta of the put option increases towards zero. The position is called a choke because it is a long, no money call and put option.
Examples of charm
As an example, suppose an investor has an out of the money call option with a delta of 15% and a normalized charm of -1. All things being equal, when the investor looks at the call the next day, the delta will be 14%.
As another example, let’s say a trader places a delta hedged call option on Friday with a charm of 1 and 15% delta; They lack 15 batches of the spot product for every 100 calls they have. By Monday at 8 am, the call delta may have decreased to 12.5%; two and a half days have passed times the charm of 1. Trader’s delta coverage is no longer accurate; they are too short of the underlying security. If the spot market opens higher on Monday, the trader has to buy back deltas to hedge his position and reestablish a neutral delta stance. Special attention is needed around the expiration time of an amulet, as it can become very dynamic.