What it means
An option's delta tells you how many shares' worth of price movement the option behaves like. A call with a delta of 0.40 gains about $0.40 for each $1 rise in the share price, so a trader holding it carries exposure similar to 40 shares per 100-share contract.
Charm measures how that delta shifts each day as the expiry date gets closer. The effect arises because time is a key input into option pricing.
As expiry approaches, an option that is out of the money (unlikely to finish with value) becomes less likely to pay out, so its delta slides towards zero, while an in-the-money option's delta moves towards one. Charm puts a number on that slide.
For a business, charm matters mostly to anyone running a hedge. A treasury team or trading desk that offsets option risk with shares or futures has to adjust the hedge as delta changes, and charm tells them in advance which way and by how much.
Ignoring it means a hedge that is correct on Monday can be noticeably wrong by Friday. Charm is a second-order measure, which means it describes the change in another Greek (delta) and not the option's price directly.
It is usually quoted per day, though some systems quote it per year, and sign conventions differ between platforms. Always check how your system defines it before comparing numbers.
The effect is strongest close to expiry and for options near the strike price, so weekends and the final days before expiry deserve special attention. Because the measure is a model output, it relies on assumptions about volatility and interest rates, and it should be treated as a guide and not a guarantee.
In practice
Real-world examples.
Example
An options desk at a regional bank hedges a book of calls on a technology share. Over a long weekend, charm shows the delta will fall, so the desk plans to buy back part of its short share position when markets reopen.
Example
A corporate treasurer holds options to hedge a commodity purchase and notices the hedge ratio keeps drifting. Her risk report includes charm, which explains that most of the change comes from time passing and not from price moves.
Example
A retail trader sells weekly put options and finds his exposure shrinking as expiry approaches. He learns that charm is steadily reducing his delta, which is why his position behaves differently on Thursday than it did on Monday.
Formula
Calculation
Charm = Change in delta / Change in time
Suppose a trader holds 50 call option contracts on a share priced at $80, with each contract covering 100 shares, which is 5,000 shares in total. The delta is 0.40, so the hedge needs to be short 5,000 x 0.40 = 2,000 shares. The charm is -0.02 per day, so after 5 days, with the share price unchanged, delta falls by 5 x 0.02 = 0.10 to 0.30. The required hedge becomes 5,000 x 0.30 = 1,500 shares, so the trader buys back 500 shares, worth 500 x $80 = $40,000.Case study
Seen in the real world.
Quayside Derivatives is an illustrative, fictional trading firm that hedged its option book once a day at the market close. Its risk team noticed a recurring loss on Mondays, even when prices had barely moved over the weekend.
The cause was charm. Two days of time decay had changed the deltas on near-expiry options, so the Friday hedge was slightly wrong by Monday morning and the firm was carrying unintended market exposure.
The team added a charm line to its daily report and began adjusting hedges on Fridays to allow for the weekend drift. The illustrative outcome was that the Monday losses largely disappeared, and the firm gained a clearer view of which positions were most sensitive to the calendar.
Watch out
Common mistakes.
- Assuming delta stays fixed until the share price moves, when charm shows it drifts every day as expiry gets closer.
- Confusing charm with theta, which measures how the option's value changes over time, whereas charm measures how delta changes over time.
- Comparing charm figures between systems without checking whether they are quoted per day or per year and which sign convention is used.
Questions
People also ask.
Why is charm called delta decay?
Because it shows the decay, or drift, of delta as time passes, in the same way theta shows the decay of the option's price.
When does charm matter most?
It matters most for options close to expiry and close to the strike price, and for hedges that must be held over weekends or holidays.
Do non-traders need to know about charm?
Usually not in detail, but anyone who relies on option-based hedges should understand that hedge sizes drift over time and need regular adjustment.
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